Strain-hardening Rate Research Articles

Texture induced planar anisotropy of dwell fatigue response in titanium: Insights from experiments and crystal plasticity simulations

This study elucidates the mechanism of texture induced planar anisotropy in ambient temperature (∼25 °C) dwell fatigue response of an annealed sheet of commercially pure titanium (cp-Ti). Dwell fatigue resistance on loading along rolling direction (RD) was observed to be markedly superior when compared to the loading along transverse direction (TD). Texture caused significant anisotropy in the strain hardening and strain rate sensitivity (SRS) which altered the dwell-fatigue response between RD and TD. RD direction had higher strain hardening and lower SRS both of which synergistically led to higher dwell-fatigue life compared to the TD direction. A combination of electron back scattered diffraction (EBSD) and Crystal Plasticity Fast Fourier Transform (CPFFT) simulations confirmed higher activity of prismatic slip in RD which led to higher strain hardening compared to TD. An analytical model was applied to deconvolute the contributions of strain hardening and SRS on dwell-fatigue life. The effect of strain hardening was observed to be higher when compared to that of SRS. The results of this work indicate that crystallographic texture is a remarkable tool to improve the dwell fatigue life of titanium.

Dynamic mechanical response and damage mechanisms of nacre-inspired 2024Al/B4C composite at elevated temperature

In this study, the nacre-like 2024Al/B4C composites with a lamellar-interpenetrated architecture, virtually free of pores and cracks, were fabricated through combining freeze casting with pressure infiltration, and their quasi-static and dynamic compressive properties were investigated over the temperature ranged from 25 to 500 °C. The dynamic compressive strength and strain were greater than quasi-static ones due to strain-rate hardening and adiabatic heating softening mechanisms. Regardless of strain rates, the compressive strength decreased with temperature, while the failure strain increased. This could be explained by four main fracture phenomena including cracking of B4C and intermetallic compounds (IMCs), matrix deformation and interfacial debonding. The matrix deformation prevailed actively at high temperatures, with a reduced overall trend towards cracking and interfacial debonding. The interfacial debonding and particle cracking acted as the dominant factors that deteriorated the compressive behavior, whereas the soften matrix induced by elevated test temperatures effectively blocked the crack propagation that favorably worked for the strain. As the temperature was raised, the softened matrix destabilized particle skeleton with the deformation behavior of the composites determined by the alloy matrix. However, recrystallization occurred within the alloy matrix, accompanied by a reduction in dislocation density, which degraded the strength of the composites. The elevated temperatures significantly enhanced the strain rate sensitivity of the composites because of the matrix softening yielding a greater proportionate enhancement of particle stress at high temperature than at low temperature.

Dynamic compressive response and impact resistance of bioinspired nacre-like 2024Al/B4C composites

In this study, the researchers constructed nacre-inspired 2024Al/B4C composites with a lamellar-interpenetrated structure using pressured infiltration of alloy melt into freeze-cast B4C scaffolds, and investigated their dynamic and ballistic properties. The defects such as pores or cracks were hardly observed, and a few intermetallic compounds (IMCs) were contained within the alloy matrix. Because of strain-rate hardening and alloy matrix melting, the dynamic compressive strength and strain were greater than quasi-static ones. The dynamic response could be interpreted by a mixture rule according to B4C volume fraction, and by main fracture phenomena such as cracking of B4C and IMCs, alloy matrix deformation, and interfacial debonding. After the ballistic test, the nacre-like composites achieved enhanced impact resistance compared to conventional Al/B4C materials, while maintaining integrity rather than breaking destructively as monolithic Al/B4C composites did, which derived from multiple energy absorption mechanisms including crack deflection, ductile-ligament bridging, and pull-out behavior. This work opens a promising new avenue for the development of advanced armor systems.

Elimination of oxygen sensitivity in \u03b1-titanium by substitutional alloying with Al

Individually, increasing the concentration of either oxygen or aluminum has a deleterious effect on the ductility of titanium alloys. For example, extremely small amounts of interstitial oxygen can severely deteriorate the tensile ductility of titanium, particularly at cryogenic temperatures. Likewise, substitutional aluminum will decrease the ductility of titanium at low-oxygen concentrations. Here, we demonstrate that, counter-intuitively, significant additions of both Al and O substantially improves both strength and ductility, with a 6-fold increase in ductility for a Ti-6Al-0.3 O alloy as compared to a Ti-0.3 O alloy. The Al and O solutes act together to increase and sustain a high strain-hardening rate by modifying the planar slip that predominates into a delocalized, three-dimensional dislocation pattern. The mechanism can be attributed to decreasing stacking fault energy by Al, modification of the “shuffle” mechanism of oxygen-dislocation interaction by the repulsive Al-O interaction in Ti, and micro-segregation of Al and O by the same cause.

Facile route to implement transformation strengthening in titanium alloys

Developing lighter, stronger and more ductile aerospace metallic materials is in demand for energy efficiency strategies. Alloys with twinning-induced plasticity (TWIP) and/or transformation-induced plasticity (TRIP) effects have been exploited to defeat the conflict of strength versus ductility, yet very few if any physically informed methods exist to address the complex interactions between the transitions. Here we report a facile route to deploy transformation-mediated strengthening in Ti alloys, which particularly focuses on the supervised activation of TRIP and TWIP via a mechanism-driven modelling approach. New alloys were comparatively developed and presented notable resistances to strain localisation, but interestingly through distinct mechanical characteristics. Specifically, extraordinary strain-hardening rate (dσ/dε) with a peak value of 2.4 GPa was achieved in Ti-10Mo-5Nb (wt.%), resulting from the synergetic activation of hierarchical transformations. An efficient model integrating TRIP and TWIP was applied to understand the interplays of the transition mechanisms.

Strain rate dependent plasticity of lithium-ion pouch cells: Experiments and simulations

The safety of electric vehicles under crash event depends on the mechanical behavior of Lithium-ion cells under large deformation at high strain rates. Here, an extensive experimental campaign is performed on large-format pouch cells under out-of-plane indentation with two indenter shapes and speeds ranging from a few millimeters per minute up to ten meters per seconds, spanning six decades of strain rates. It reveals that the displacement at the onset of short circuit decreases with increasing strain rates, while a non-monotonic relationship is observed between the strain rate and the maximum force as well as the macroscopic cell tangent stiffness. Based on the experimental results, a phenomenological constitutive model is proposed making use of a Deshpande-Fleck yield locus and strain-rate dependent hardening. An internal variable is introduced to capture the softening at intermediate strain rates. The calibrated model is able to accurately reproduce the experimental data and is further validated on a hemispherical indentation performed at two meters per seconds.

The role of viscous regularization in dynamical problems, strain localization and mesh dependency

Strain softening is responsible for mesh dependence in numerical analyses concerning a vast variety of fields such as solid mechanics, dynamics, biomechanics and geomechanics. Therefore, numerical methods that regularize strain localization are paramount in the analysis and design of engineering products and systems. In this paper we revisit the elasto-viscoplastic, strain-softening, strain-rate hardening model as a means to avoid strain localization on a mathematical plane (“wave trapping”) in the case of a Cauchy continuum. Going beyond previous works (de Borst and Duretz, 2020; Needleman, 1988; Sluys and de Borst, 1992; Wang et al., 1997), we assume that both the frequency ω and the wave number k belong to the complex plane. Therefore, a different expression for the dispersion relation is derived. We prove then that under these conditions strain localization on a mathematical plane is possible. The above theoretical results are corroborated by extensive numerical analyses, where the total strain and plastic strain rate profiles exhibit mesh dependent behavior.

Uncovering the mechanical behavior of twisted carbon nanotube assemblies under high-speed stretching

Twisted carbon nanotube (CNT) fibers are regarded as an effective assembly for intelligent actuators and artificial muscles, which are inevitable to encounter high-speed collision and impact. In order to reveal the dependence of high-speed mechanical performance on the CNT assembly, the dynamic failure behaviors of untwisted and twisted CNT assemblies under instant stretching are investigated with experimental and numerical methods. The strength of the untwisted and loosely-packed CNT ribbon is more sensitive to strain-rate than densified and twisted CNT fiber owing to its interlaced CNT network. The numerical results demonstrated that the evolution of interior flaws governed the mechanical behavior under different stretching rates. The instant stretching does not allow an efficient stress distribution within the limited time, and thus hinders the flaw evolution, leading to the cascade-like failure mode and a strain-rate hardening effect. It is inferred that the rate-dependent sensitivity may be attributed to the twisted microstructure and untwisted CNT ribbon. This work on the dynamic behavior of twisted CNT ribbon/fiber can help to design the twisted structure under the high-speed applications.

Deformation behavior of a Co-Cr-Fe-Ni-Mo medium-entropy alloy at extremely low temperatures

We report the mechanical and microstructural characteristics of a medium-entropy alloy, Co17.5Cr12.5Fe55Ni10Mo5 (atomic percent, at%) at cryogenic temperatures, down to a record low temperature of 0.5 K. The alloy exhibits excellent strength and ductility combined with a high strain-hardening rate in the entire temperature range investigated. Its property profile, including the yield strength, ultimate tensile strength, strain hardening capability, and absorbed mechanical energy, is better than those of most alloys and HEAs used in cryogenics. Within the interval of extremely low temperatures considered (0.5–4.2 K), the alloy exhibits several unusual features, including anomalies of the temperature dependence of the yield strength and tensile ductility, discontinuous plastic deformation (DPF), and a change in the propensity for the deformation-induced martensitic transformation. While the occurrence of these effects in the same temperature interval may be fortuitous, we hypothesize that they are interrelated and provide a tentative explanation of the observed phenomena on this basis.

Strain Hardening and Stretch Formability Behavior of Triple Phase (TP) Steel Strips

The current work explores the strain hardening and stretches formability behaviour of the developed Triple Phase (TP) steel. Double quenched TP steel strips posse three distinguished stages of strain hardening on tensile forming. 1st stage represents the highest n-value reflecting resistance to homogeneous deformation, where steel can be safely stretched. 2nd and 3rd stage reveals lower n-values, where localized thinning exist. On Erichsen testing, the relationship between punch forming force and punch stroke exhibits two forming regions. The 1st region is delineated by a straight line showing an ultra-high strain-hardening rate, which represents a reversible elastic stretch forming. The 2nd forming region continues to a higher Erichsen punch stroke than that of the 1st region and presents the permanent plastic stretch forming behaviour. It is found that bainite and martensite clusters created, by double quenching, in TP-steel exaggerated the elastic stretch forming limit 10 times higher than the as-hot rolled condition. 7 min. holding time of strips in the salt bath is considered the most effective for the creation of a useful volume fraction of the bainite phase. However, 21 min. holding time in salt bath grows martensite laths through the bainite aggregates, affecting negatively on stretch formability.

Elevated temperature ductility dip in an additively manufactured Al-Cu-Ce alloy

The deformation and failure mechanisms of Al-9Cu-6Ce (wt%) based alloys fabricated with laser powder bed fusion were investigated from room temperature to 400°C. The yield and ultimate tensile strengths decreased monotonically with increase in temperature, but the tensile elongation dipped unexpectedly at elevated temperatures and exhibited a minimum at 300°C. The dip in tensile elongation occurred with a concomitant dip in strain-rate sensitivity (SRS) of deformation. The as-fabricated alloy microstructure was heterogeneous, and the heat affected zone (HAZ) underneath the melt pool boundary was prone to strain localization. At 300 °C, the reduced SRS promoted the progression of strain localization in the HAZ leading to failure initiation and the dip in tensile elongation. A higher SRS or strain-hardening rate at other temperatures improved the tensile elongation by slowing the progression of strain localization in the HAZ such that failure initiated by other mechanisms elsewhere in the microstructure. Notably, the tensile elongation was limited by the defect structure only in a narrow temperature range (150 - 200 °C) while at other temperatures it was limited by the inherent microstructural features. This investigation exemplifies unexpected deformation and failure mechanisms possible in heterogeneous microstructures that result from additive manufacturing.

Superior strain-hardening by deformation-induced nano-HCP martensite in Fe–Mn–Si–C high-manganese steel

We propose that high strain-hardening in face-centered cubic (FCC) crystals containing interstitial atoms could be achieved through the formation of nanoscale hexagonal close-packed (HCP) martensite with severe lattice distortions. Our experimental results showed that carbon atoms could more effectively prevent the HCP martensite from thickening and result in the formation of nano-HCP martensite. This caused a higher strain-hardening rate in FeMnSiC steel with heavy carbon than in FeMnSiCrNi steel with trace carbon though the HCP martensite transformation kinetics was almost the same in these two steels.

Dynamic impact behavior and deformation mechanisms of Cr26Mn20Fe20Co20Ni14 high-entropy alloy

In this work, the dynamic impact behavior and linked deformation mechanisms of a Cr26Mn20Fe20Co20Ni14 high-entropy alloy (HEA) with face-centered cubic structure were systematically explored. The HEA displays uniform plastic deformation without any adiabatic shear bands at a strain rate range from 1000 to 3000 s−1. Moreover, the yield strength exhibits a pronounced strain rate dependence, increasing by 28% from 282 MPa at 1000 s−1 to 360 MPa at 3000 s−1. The strain hardening exponent, strain rate sensitivity and temperature rise were calculated to be 0.899–0.95, 0.076 and 64.7 K, respectively, indicative of high strain and strain-rate hardening capabilities and strong resistance to thermal softening induced adiabatic shear localization. Detailed microstructural analyses decipher a transition of deformation mechanism from dislocation slip at 1000 s−1 to stacking faults (SFs) at 2000 s−1 and further to twinning at 3000 s−1, respectively. The strengthening mechanisms are delineated as manifold interactions between glide dislocations and SFs, SFs and SFs (i.e. the Lomer-Cottrell locks), and SFs and twins. Our work provides a comprehensive understanding on the dynamic impact behavior, deformation and strengthening mechanisms of Cr26Mn20Fe20Co20Ni14 high-entropy alloy.

TRIP-assisted compressive ductility in Ti-rich Ti60Mo10V10Cr10Zr10 refractory medium-entropy alloy

Compositional tuned non-equiatomic refractory high-entropy alloys are coveted materials as they achieve considerable plasticity through transformation-induced plasticity (TRIP) behavior. In this study, a novel Ti-rich Ti60Mo10V10Cr10Zr10 refractory medium-entropy alloy (RMEA) was designed using FactSage. The plastic deformation of the alloy produced using vacuum arc remelting was investigated through a room-temperature compression test at different strain rates. A high strain-hardening rate and an m-value of 0.031 were observed in the Ti-rich Ti60Mo10V10Cr10Zr10 RMEA. The dimple structures formed in BCC phases and TRIP-assisted deformation attribute to the strength and ductility trade-off in Ti-rich Ti60Mo10V10Cr10Zr10 RMEA.

Size-dependent plasticity of hetero-structured laminates: A constitutive model considering deformation heterogeneities

Deformation mechanism-based constitutive modeling can serve as a flexible tool to optimize the microstructure of hetero-structured metals for achieving better mechanical performance. In this work, a dislocation density-based constitutive model, which considers geometrically necessary dislocations (GNDs) and the back stress induced by internal heterogeneous deformation, is developed for describing the deformation of hetero-structured laminate materials. The heterogeneous laminates are considered to consist of alternating coarse-grained and nano-grained layers separated by extended interfaces (interface affected zones, IAZs). The respective deformation mechanisms of each phase are established based on experimental information. The evolution laws of back stress and GNDs for the coarse-grained layers, nano-grained layers and IAZs are formulated within a unified framework based on dislocation pile up theory. The simulated tensile responses are in quantitative agreement with experimental data for heterogeneous copper/bronze laminates with different interface spacings and different volume fractions of the nanostructured layers. The model also allows to represent the back stress and strain-hardening rate accurately. It is found that smaller interface spacing, implying a higher volume fraction of the IAZ, leads to a higher density of GNDs and more significant back stress. The IAZ is demonstrated to be the key to understanding the strength-ductility combination of laminates. The developed model can be readily applied to other kinds of metallic materials with architectured microstructures.

Investigation and mean-field modelling of microstructural mechanisms driving the tensile properties of dual-phase steels

A hybrid composite medium-field (Hy-MFC) model was developed to predict the tensile properties of dual-phase steels under monotonic loading based on physical parameters of the microstructure (phase fraction, chemical composition, and grain size of each phase). The Hy-MFC model is intended to be applicable to a wide range of fully ferritic to fully martensitic steels, particularly for alloy design and production-line monitoring. Accounting for the prior austenitic grain size as well as the chemical composition of martensite in the model resulted in good agreement between the modelling and experimental data for the investigated industrial and ternary steels with various martensite fractions. In addition, electron backscatter diffraction monitoring performed during tensile tests allowed to understand the different interactions necessary to reproduce the macroscopic hardening of dual-phase steels. In particular, a hybrid scaling transition law was proposed to reproduce the strain-hardening rate for small deformations for bi-percolant microstructures.

High strain rate effect on tensile ductility and fracture of AM fabricated Inconel 718 with voided microstructures

The paper describes Electromagnetic Ring Expansion Tests (ERET) performed on Laser Melting Powder Bed Fusion (LPBF) Inconel 718 stress relieved test pieces, to establish the effect of a randomly dispersed spherically voided microstructure on tensile ductility, fracture, and fragmentation at high strain rate (10−3 < ε < 104 s−1). An empirical model to predict porosity type and growth rates as a function of laser energy density was established, to select the LPBF process parameters to fabricate test pieces under stable conduction and keyhole melting. The size, shape, distribution of macro and keyhole pores in the test pieces obtained for ERET testing were characterised. At high strain rate the number of ring fragments for the highest porosity doubled, accompanied by a reduction in true strain at maximum uniform elongation and fracture strain. The trend for reducing fracture strain with increasing porosity at high strain rate was described by a decaying power law. Overall, there was a significant positive strain rate effect on tensile ductility at lower porosities attributed strain rate hardening (Hart, 1967) [1]. Fracture surfaces containing the highest porosity identified four different void coalescence mechanisms that helped explain the influence of larger pores on the stress state in the alloy.

Analytical modelling of edge chipping in scratch of soda-lime glass considering strain-rate hardening effect

Soda-Lime Glass (SLG) has been widely used in the creation of highly-functionalised optical devices. However, machining of SLG easily resulted in various defects. Among these defects, edge chipping (EC) can be treated as the most damageable in terms of both mechanical properties and optical performances. Although efforts have been paid to this topic, previous investigations (i) focused on edge chipping in low strain rate, which was 101-102 times lower than the ones in real machining, (ii) assumed edge chipping shape as circular, while the experiments in this work proved this assumption might be inaccurate in high strain rate circumstances, and (iii) were experimental efforts, resulting in limited knowledge of process principles. To fill this gap, this paper aims to propose an analytical model to calculate the size and the shape of edge chipping in scratch of soda-lime glass with the special consideration of strain-rate hardening effect. A series of experimental trials were performed to validate the model accuracy under different parameters. The details in scratching process were discussed by force analysis. A typical model application was given as well, which was designing the machining strategy based on the proposed model so that a required region with limited edge chipping can be obtained. Considering the research gaps mentioned above, the key findings in this paper are expected to be meaningful and helpful to provide references in the real fabrication of high-valued optical devices made of SLG.

Effects of temperature and strain rate on the tension-compression asymmetric plastic deformation behavior of ME20M magnesium alloy: Experiments and modeling

The tension-compression asymmetry of a rare-earth-containing alloy sheet, ME20M, is experimentally investigated along the rolling direction over a wide strain-rate range from 0.001 to 2500 s−1 and at temperatures from 213 to 488 K. The asymmetry of yield stress in tension and compression decreases with increasing temperature and decreasing strain rate. The strain-rate sensitivity of the tension-compression asymmetry during the plastic deformation stage increases with increasing temperature. It is observed that the compressive strain-hardening rate is much higher than the tensile one due to more {101-2} tension twins occurring in the compressive plastic deformation. A viscoplastic self-consistent (VPSC) model is employed to simulate the tensile and compressive stress-strain responses, deformation texture, and deformation mechanism evolution over wide ranges of strain rates and temperatures. Results indicate that the VPSC model is capable of capturing the macroscopic plastic deformation characteristics of ME20M alloy. Tensile plastic deformation is dominated by slip at strain rates up to 103 s−1, and basal slip and tension twinning are the main deformation modes in compressive plastic deformation. Effects of strain rate and temperature on the main plastic deformation mechanism of ME20M alloy are insignificant within the tested rate and temperature ranges.

Effect of nickel on hardening behavior and mechanical properties of nanostructured bainite-austenite steels

Ni-free and Ni-bearing steels were designed to elucidate the effect of Ni on the free energy of bainitic transformation. Steels with two distinct nano-bainite structures were obtained through conventional one-stage and two-stage isothermal treatments. The effect of work hardening and accompanying strain on martensitic transformation of the two nano-bainite structures was also studied. Microstructure of both the steels consisted of bainitic ferrite and film-like and block-like retained austenite (RA). The total carbon concentration, degree of Fe–C cluster formation, and stability of RA were significantly affected by the free energy of bainitic transformation. The presence of Ni leads to reduction in the free energy of bainitic transformation, refinement of bainite structure, and extension of bainite nucleation regime. The carbon-content in block-like and film-like RA microstructure of Ni-bearing steel was 5.5% and 19.1%, respectively, which was greater than Ni-free steel. The load-displacement behavior indicated superior strain hardenability and higher strain hardening rate (SHR) in Ni-bearing steel. The uniform nanostructure of Ni-bearing steel promoted the formation of stable film-like RA between bainitic ferrite, leading to higher strain hardening rate and stronger transformation-induced plasticity (TRIP) effect at large strain. The Ni-bearing steel was characterized by superior plasticity (13.7%–10.3%) and product of tensile strength and % elongation (25.9 GPa·% to 20.9 GPa·%) in comparision to the Ni-free steel.