Strain Rate Domain Research Articles

Fatigue S-N curve approach for impact loading of hyper- and visco-elastic leading edge protection systems of wind turbine blades

Computational evaluation of leading edge erosion remains challenging due to the high-strain rate loading conditions caused by impact of the wind turbine blade leading edge with rain droplets and other environmental particles. Here, a methodology is proposed for obtaining an S-N curve which can be used for impact fatigue evaluation of hyper- and viscoelastic leading edge protection systems for wind turbine blades, in the relevant strain rate domain. Two material systems (hard and soft polyurethane (PU)) are characterised experimentally by dynamic mechanical analysis (DMA) and static tensile tests. Time-temperature superposition is applied to the raw DMA data in order to obtain the material’s mastercurve, describing its visco-elastic behaviour in an expanded strain rate domain. The Yeoh (hyperelastic) and prony series (vis-coelastic) material model parameters are calibrated and form the input for a 2D-axisymmetric finite element model, in which Single Point Impact Fatigue Test (SPIFT) testing conditions are simulated. The stress field experienced by the coating during SPIFT testing is obtained and combined with the experimental measurements, allowing the determination of the material systems S-N curve, in the relevant strain rate domain. Results for a hard and soft PU coating system are compared with rain erosion test (RET) data. The RET data shows higher lifetime for the hard PU systems, a tendency that can be predicted when comparing the S-N curve for the hard and soft PU system. This methodology can be utilised in computational lifetime evaluation of leading edge coating systems. Furthermore, the methodology has the potential to partly alleviate the need of RET in the development and comparison of next-generation leading edge protection systems.

Effect of temperature and strain rate on the deformation behaviour and microstructure of Al0.7CoCrFeNi high entropy alloy

The high-temperature deformation behaviour of Al0.7CoCrFeNi alloy was studied at 800–1100 °C and 0.01–10 s−1. The alloy exhibited extensive softening via recrystallization and recovery with the examined temperature and strain rate domains. The recrystallization mechanism in the FCC phase was geometric dynamic recrystallization, and that in the BCC/B2 phase was continuous dynamic recrystallization. Further, the BCC/B2 lamellae underwent fragmentation via boundary splitting and termination migration. The amount of softening and subgrain morphology were dependent on the crystallographic orientation of the grains prior to deformation. Apart from lamellar fragmentation, dynamic globularization of BCC/B2 phase was found in certain grain colonies. Compared to heat treatment, hot deformation improved the globularization kinetics. Further, BCC/B2 precipitation occurred along the grain boundaries and at the triple points of the recrystallized FCC phase. However, the overall BCC/B2 phase fraction remained constant. Post-deformed alloy was also characterized by preferential cracking along the allotriomorphic FCC phase boundaries. The difference in strength between the idiomorphic and allotriomorphic regions was attributed to this grain boundary cracking. The activation energy for deformation showed a direct dependency on temperature and strain rate but an inverse relationship with strain.

Exploring the Effect of Dispersed Phase on the High Strain Rate Mechanical Response of Nanosilica Dispersions

Shear Thickening Fluids (STFs) constitute a special class of materials which exhibit phase transition from low to high viscosity state when exposed to shearing forces, particularly, when the applied shear rate exceeds a critical value. The last decade has witnessed a mutual symbiotic relationship between STF and high-performance fabrics such as Kevlar®, Dyneema®, Ultra High Molecular Weight Polyethylene (UHMWPE) etc., to produce new light weight and flexible protective materials systems with enhanced knife, stab and ballistic resistant properties than the existing ones. In this study, we explore the effect of particle shape and size on the high strain rate dynamic response of nanosilica dispersions. Shear thickening fluid (STF) was synthesized using fumed silica and spherical nanosilica particles, comprising the dispersed phase, whereas PPG400 (Polypropylene Glycol) was used as the dispersion medium. Ultrasonic homogenization technique was used for the synthesis of STF. The low strain rate rheological characterization was conducted on MCR302 rheometer at 25°C, whereas the high strain rate characterization was performed on inhouse designed and developed SHPB (Split Hopkinson Pressure Bar) apparatus. Fumed silica (FS) particles possess high specific surface area owing to their fractal structure. Therefore, their low molecular weight dispersions exhibit shear thickening behavior thus making them potential candidates for liquid body armour applications. On the other hand, spherical silica dispersions exhibit shear thickening behavior in high phase volume concentrations. Experimental studies showed that spherical silica based STF dispersions exhibited enhanced shear thickening in the low strain rate domain, as well as better mechanical response in terms of higher peak stress under high strain rate compressive loading conditions, during SHPB testing, in comparison to their fumed silica counterpart. Thus, it can be inferred that the mechanical response of nano-silica dispersions is influenced by the shape of the particles constituting the dispersed phase.

Three-dimensional hot processing map of a nickel-based superalloy (Alloy 925) established by modified artificial neural network model

The hot deformation behavior of Alloy 925 in the temperature range of 900–1150 °C and strain rate range of 0.01–10s−1 was investigated through the isothermal hot compression tests. Based on the artificial neural network model, the stress distribution in the three-dimensional (3D) space consisted of deformation condition parameters was reconstructed. Afterwards, the 3D distribution maps of strain rate sensitivity (m) and power dissipation efficiency (η) were proposed to reveal the effect of deformation parameters on the hot workability. Furthermore, a novel 3D processing map was established by combining the traditional dynamic materials model and the corresponding data set. Through the microstructural characterization, it can be found that the instability regions exhibit inhomogeneous microstructure with massive distorted grains and few dynamic recrystallization (DRX) grains, while the stable regions are characterized by various DRX mechanisms, including discontinuous dynamic recrystallization, continuous dynamic recrystallization, and twin-DRX. Noteworthily, the relatively low η-value (<22%) was revealed in the high temperature-high strain rate domain caused by substantial occurrence of DRX. Finally, the optimum processing parameters at the true strain of 0.85 can be determined to be 970–1150 °C and 0.01–1.08s−1 with the η-value of 30.6–42.3%. In contrast, the construction method of novel 3D processing map can effectively avoid data distortion and also demonstrate a better validity for predicting hot workability. Through the present work, the feasibility of artificial neural network for learning complex hot deformation behavior has been illustrated. It not only has better prediction of typical microstructure, but also can reproduce the adiabatic heating law, which is convenient to be used in actual industrial production.

Nucleation properties of isolated shear bands.

Shear banding, or localization of intense strains along narrow bands, is a plastic instability in solids with important implications for material failure in a wide range of materials and across length scales. In this article, we report on a series of experiments on the nucleation of single isolated shear bands in three model alloys. Nucleation kinetics of isolated bands and characteristic stresses are studied using high-speed in situ imaging and parallel force measurements. The results demonstrate the existence of a critical shear stress required for band nucleation. The nucleation stress bears little dependence on the normal stress and is proportional to the shear modulus. These properties are quite akin to those governing the onset of dislocation slip in crystalline solids. A change in the flow mode from shear banding to homogeneous plastic flow occurs at stress levels below the nucleation stress. Phase diagrams delineating the strain, strain rate and temperature domains where these two contrasting flow modes occur are presented. Our work enables interpretation of shear band nucleation as a crystal lattice instability due to (stress-assisted) breakdown of dislocation barriers, with quantitative experimental support in terms of stresses and the activation energy.

Compressive Flow Behaviour and Deformation Instabilities of Fe-Mn-Al-Ni-C Lightweight Duplex Steel

In this work, uniaxial hot compression tests of Fe-Mn-Al-Ni-C steel are conducted in the domain of strain rates (0.001–10 s−1) and temperatures (1223–1423 K). The apparent activation energy of the present steel is estimated as ~400 kJ mol−1. A constitutive equation is formulated by using the experimental flow stress data to depict the flow characteristics of the steel. An excellent correspondence (R = 0.99 and AARE = 5.2%) between the experimental and predicted flow stress data has been obtained. Further, we have predicted the deformation instabilities in the present steel based on the various existing criteria (viz. Prasad, Gegel, Alexander, Jonas, and Semiatin). The predicted unstable domains are further validated by the microstructural characterization. The instability features like boundary decohesion, micro-cracks, and flow localization are observed in the regions 1223 K/0.1–10 s−1 and 1273–1373 K/1–10 s−1 while the wedge-cracks at the triple junctions of the boundaries are observed in the region 1350–1423 K/0.001 s−1. The Prasad’s instability criterion could precisely identify the flow instabilities in the present steel. However, the Gegel’s and Alexandar’s criteria over-estimated the unstable regions (<1300 K/0.003–0.1 s−1), (1300–1373 K/0.003–1 s−1) and (1373–1423 K/0.002–5.62 s−1) in the material. The Jonas’ and Semiatin’s criteria, on the other hand, underrated the extent of flow instabilities in the lightweight duplex steel.

Grain Boundary Sliding and Strain Rate Sensitivity of Coarse and Fine/Ultrafine Grained 5083 Aluminum Alloys

The viscoplastic behavior of coarse and bimodal fine/ultrafine grained (F/UFG) Al5083 alloy was investigated between 20 °C and 200 °C through tensile tests at various strain rates, and stress relaxation tests to deduce the strain rate sensitivity (SRS). The plastic strain fields were measured by correlation of SEM images. In the F/UFG material at high temperature, very high strains were measured in shear bands which sometimes crossed the whole gage width and exhibited intensive grain boundary sliding (GBS). Both the SRS and ductility rose with the temperature, and as the strain rate decreased, mainly due to a rising contribution of GBS, which accommodated a much larger fraction of the global strain in the F/UFG material. The boundary between the temperature–strain rate domains where grain refinement led either to strengthening or to softening was determined. Finite element simulations of tension and relaxation tests with viscoplastic grains and sliding grain boundaries captured the macro-scale behavior of the F/UFG material. It also provided some insight into the mechanisms of correlated and cooperative GBS and grain rotation along percolation paths (both inter and intragranular), probably, responsible for macro shear banding.

Influence of phase composition on Portevin-Le Chatelier effect in Al-Mg alloys

The temperature-strain rate domain of the Portevin-Le Chatelier (PLC) effect has been determined for three ultrafine grained aluminum alloys: Al-3Mg (A1), Al-4,57Mg-0,35Mn-0,2Sc-0,09Zr (A2) and Al-5,4Mg-0,52Mn-0,1Zr (A3) (wt.%). The apparent activation energy of the serrated yielding was estimated. It was found that the presence of dispersed particles leads to a decrease in the activation energy and the temperature–strain rate domain of the PLC effect becomes narrower.

Superplastic behavior of a powder metallurgy superalloy during isothermal compression

In this work, the flow behaviors and microstructure evolution of a powder metallurgy nickel-based superalloy during superplastic compression is investigated. Based on the strain rate sensitivity m determined by flow data, superplastic region is estimated at relatively low temperature and strain rate domains, specifically around 1000 °C/10−3 s−1. Thereafter, the cylinder specimens are isothermally compressed at 1000 °C/10−3 s−1 and 1025 °C/10−3 s−1 with different strains, to exam the superplasticity and related mechanisms. The experimental results indicate that the accumulated dislocations are mainly annihilated by dynamic recovery and dynamic recrystallization (DRX), and the grain boundary sliding (GBS) contributes to the total strain during superplastic compression as well. In addition, the cavities and cracks at triple junctions or interfaces between matrix and second phase particle have not been detected, which is different from superplastic tensile deformation.

Effect of initial microstructure and beta phase evolution on dynamic recrystallization behaviour of Ti6Al4V alloy - An EBSD based investigation

The use of Ti6Al4V alloy in critical aerospace applications among other titanium alloys is higher due to the high strength, toughness and corrosion resistance characteristics. Achieved combination of strength and toughness is directly related to the bimodal (equiaxed alpha plus transformed beta) microstructure obtained by hot working of this alloy in a narrow strain rate and temperature domain. Present study distinctly describes the evolution of microstructure during hot deformation as an effect of process conditions and initial microstructure characteristics of Ti6Al4V alloy. The initial microstructure and processing conditions significantly influenced the evolution of β phase and dynamic recrystallization behaviour. An increase in β phase fraction was observed due to the increased adiabatic temperature at higher strain rates during α+β working. The increase in volume fraction of stable β phase as result of vanadium diffusion during hot working revealed the existence of strain induced phase transformation. Continuous dynamic recrystallization (CDRX) led to the fragmentation of initial α grains, and the effect of initial grain orientation on the CDRX mechanism was studied. The initial grains with the basal plane parallel to the compression direction revealed large fragmentation due to the high resistance to deformation. A CDRX mechanism map was developed based on the effect of processing conditions and initial grain characteristics.

Hot deformation of high-Nb-containing γ-TiAl alloy in the temperature range of 1000–1200 °C: microstructural attributes to hot workability

Hot deformation behavior of a high-Nb-containing cast γ-TiAl-based Ti–45Al–8Nb (at.%) alloy has been investigated in the temperature range of 1000–1200 °C and the strain rate range of 0.5–0.005 s−1. The alloy shows an initial microstructure of coarse lamellar ((α2 + γ) and (γ + γ)) colonies. The effect of strain rate and temperature domain on hot deformability of the alloy has been analyzed through a correlation between the apparent activation energy, deformation process maps, and associated microtextural development. The relatively higher apparent activation energy (Q = 553.8 kJ/mol) could be correlated with the fully lamellar α2 + γ microstructure which posses greater resistance to the mobile dislocation. The results are further corroborated by the “instability-dominated” processing maps indicating poor hot deformability of the alloy in the studied temperature–strain rate range. Detailed electron microscopy of the deformed samples indicates that poor workability exhibited as cracks that are predominantly found at the coarse γ-TiAl grains situated at the lamellar boundaries. The crack initiation and propagation mechanisms during hot compression have further been discussed with reference to concurrent dynamic recrystallization. It has been found that “wedge-type” cavitation damage is prevalent during compressive deformation in the temperature range studied here. Such cracking behavior is elucidated in light of the “Semiatin–Seetharaman criterion.”

Hot deformation behavior of the high-entropy alloy CoCuFeMnNi

Abstract

On the constitutive modeling of a powder metallurgy nanoquasicrystalline Al93Fe3Cr2Ti2 alloy at elevated temperatures

The flow behavior of nanoquasicrystalline $$\hbox {Al}_{93}\hbox {Fe}_{3}\hbox {Cr}_{2}\hbox {Ti}_{2}$$ alloy at different strain rates and elevated temperatures was represented by the Johnson–Cook model, a modified Johnson–Cook model, a newly modified Johnson–Cook model, and a modified Zerilli–Armstrong model. A comparative study on the capability of the four models to accurately predict the flow stress of the alloy at hot deformations is made using standard statistical parameters correlation coefficient (R) and average absolute relative error (AARE). The results show that the newly modified Johnson–Cook model provides predicted stresses that agree very well with the experimental stresses at the tested domain of strain rates and temperatures, with R = 0.979 and AARE = 7.78%. The modified Zerilli–Armstrong model might predict the flow stress of the alloy but at some of the tested domain of strain rates and temperatures, with R = 0.951 and AARE = 9.13%. The Johnson–Cook model and the modified Johnson–Cook model are found to be inadequate to predict the flow stress of the alloy with R of 0.924 and 0.935 and AARE of 12.72% and 10.73%, respectively.

Study on the Low and High Strain Rate Behavior of Fumed Nano Silica Dispersions

Shear Thickening Fluids (STFs) are a special class of field responsive non-Newtonian fluids which exhibit transition from low viscosity to high viscosity state when they are subjected to shearing deformation above the critical shear rate (CSR). Due to this unique characteristic of STFs, these have found application in ballistics, especially in the development of special class of body armors called Liquid Body Armors (LBAs) which are lighter in weight and more flexible as compared to conventional heavy armours. Fumed silica (FS) is a rheologically significant material as it is a well known viscosity modifier owing to its fractal structure, and is generally used in paints, coatings, sealants, printing inks etc. In this study, two different grades of FS (A-130 and A-150) were used for the synthesis of STFs. The low strain rate studies were conducted on cone and plate rheometer and high strain rate experiments were accomplished on split Hopkinson pressure bar (SHPB) set up. The colloidal dispersions in PPG-400 (Poly Propylene Glycol 400) were synthesized using ultrasonic homogenization technique. From the experiments it was observed that A-150 fumed silica dispersion exhibited higher severity in shear thickening in the low strain rate domain, whereas A-130 fumed silica dispersion exhibited higher specimen stress and compressional strain rate under high strain rate dynamic compressive loading. Thus, it can be inferred that the same material may exhibit different behaviors in the low and high strain rate regimes. Therefore, both the studies play a vital role to completely characterize the material, especially when the material has to be subjected to ballistic applications.

Dependency of rate sensitive DRX behaviour on interstitial content of a Fe-Cr-Ni-Mo alloy

In the present work the commonly stated but not explicitly demonstrated association between the chemical composition of a material, its stacking fault energy (SFE) and dynamic recrystallization (DRX) behaviour, is established using thermo-mechanical testing, microstructural characterization and thermodynamic calculations on a Fe-Cr-Ni-Mo model alloy with varying interstitial content (0.1 < (N + C) < 0.25 wt%). The thermodynamic calculation shows that SFE decreases from 27 mJ/m2 to 17 mJ/m2 with increase in interstitial content at room temperature. The values of SFE rise upto 205 mJ/m2 to 200 mJ/m2 at 1323 K. The alloy with minimum interstitial content and maximum SFE exhibits a sluggish DRX behaviour in the strain rate domain 0.1–1 s−1. The sluggishness gradually diminishes as the interstitial content is increased and SFE is decreased. The rate-dependency of nucleation is explained on the basis of interstitial content, which changes the SFE. The present investigation also elucidates the rate- dependent grain growth for the model alloy.

Flow characteristics and hot workability studies of a Ni-containing Fe‑Mn‑Al‑C lightweight duplex steel

The high temperature deformation behavior of Fe‑9Al‑10Mn‑4Ni‑0.7C duplex steel has been investigated in the range of temperatures 1223–1423 K and strain rates 0.001–10 s−1. The multistage work hardening behaviors are analysed using Kocks-Mecking model and the correlations among various characteristic parameters of dynamic softening (viz. peak stress, recovery stress, steady-state stress and critical stress/strain) are evaluated. The processing and activation energy maps are constructed to identify the optimum processing domains. The microstructural responses towards various processing parameters are considered to correlate the dynamic softening phenomena and high efficiency domain of the processing map. The optimum hot working domain is obtained as 1223–1350 K and 0.001–0.01 s−1 which is identified by low apparent activation energy value and dominant continuous dynamic recrystallization mechanism in where typical transition of low-angle to high-angle boundary is observed. At lower temperature (<1373 K) and higher strain rate (≥1 s−1) unstable domain, material exhibits micro-bands and cracks along the austenite/ferrite interphase boundaries. Furthermore, at lower strain rate (0.001 s−1) and higher temperature (≥1373 K) unstable domain, wedge crack at the triple junction is revealed as the sign of deformation instability.

Isothermal forging of titanium aluminides without beta-phase — Using non-equilibrium phases produced by spark plasma sintering for improved hot working behavior

This paper investigates the hot forgeability of a TNB-V5 (Ti–45Al–5Nb–0.2B–0.2C, at.%) alloy produced by spark plasma sintering (SPS) from pre-alloyed powder particles using the concept of processing maps. For the first time in this paper, to the best of our knowledge, we report the possibility of the isothermal forging of a TiAl alloy without the necessity to induce the ductile β-phase in the microstructure, by using non-equilibrium phases produced by SPS. At room temperature, the SPSed sample reveals a homogeneous equiaxed microstructure consisting of globular α2-and γ-grains with the α2-phase formed mainly at the necks between powder particles as confirmed by EBSD analyses. The necks contain a lower Al content and thus transform into α-phase upon heating to forging temperature. A stable plastic flow is observed for all ranges of the studied strain rates. The presence of a fine equiaxed microstructure at hot working temperature seems to ensure good workability and leads to a relatively wide processing window. The processing map reveals two safe processing windows for the studied alloy. The lower strain rate domain (10−3-10−2 s−1) corresponding to a strain rate sensitivity value of ≈0.8 represents superplasticity of the fine and uniform (α+γ) equiaxed microstructure. The higher strain rate domain (10−2-10−1 s−1, T > 1215 °C) with a strain rate sensitivity value of ≈0.45 represents dynamic recrystallization of the α-grains at elevated temperatures. The processing map also exhibits a domain of flow instability represented by the deformation conditions of T < 1215 °C and ε˙ > 10−2 s−1, which might result from the void formation and/or cracking. Although the TNB-V5 alloy was not designed for forging operations, the SPS process can create a homogeneous equiaxed microstructure consisting of globular α- and γ-grains decorating the interfaces and triple junctions between former powder particles leading to a good hot workability. The current study offers a new process design strategy by opening up the possibility of using local non-equilibrium conditions in the material during the forging process, which could stabilize the ductile phases locally.

Constitutive modeling for high temperature flow behavior of a high-strength manganese brass

The hot compressive deformation behaviors of ZHMn34-2-2-1 manganese brass are investigated on Thermecmastor-Z thermal simulator over wide processing domain of temperatures (923–1073 K) and strain rates (0.01–10 s–1). The true stress–strain curves exhibit a single peak stress, after which the stress monotonously decreases until a steady state stress occurs, indicating a typical dynamic recrystallization. The analysis of deviation between strain-dependent Arrhenius type constitutive and experimental data revealed that the material parameters (n, A, and Q) for the ZHMn34-2-2-1 manganese brass are not constants but varies as functions of the deformation conditions. A revised strain-independent sine hyperbolic constitutive was proposed, which considered the coupled effects of strain rate temperature and strain on material parameters. The correlation coefficient and the average absolute relative error are used to evaluate the accuracy of the established constitutive model. The quantitative results indicate that the proposed constitutive model can precisely characterize the hot deformation behavior of ZHMn34-2-2-1 manganese brass.

Path-dependent work and energy in large amplitude oscillatory shear flow

Two methods are widely used to quantitatively analyze the nonlinear stress in large amplitude oscillatory shear (LAOS) flow; one is to analyze the stress in time domain and the other in strain or strain rate domain. Distinguished from these two methods, this paper exploits the concept of work and energy to analyze the oscillatory shear stress. The inner area in the strain-stress Lissajous curve after one cycle is known to be related with work, and that of the strain rate-stress Lissajous with energy. To precisely analyze the nonlinear stress, it helps to consider work and energy not only after a complete cycle but also during the cycle. In this paper, we trace the work and energy during the oscillation, together with their derivatives. We apply this concept to perfectly elastic solid, purely viscous liquid, and viscoelastic fluid. By this approach, it is shown that a rheological behavior such as strain thinning can be originated by various origin in the perspective of work and energy, which means that the rheological behavior can be subclassified in terms of work and energy. This approach is useful because it can analyze nonlinear stress without mathematically intriguing higher harmonics and it can be easily applied to any type of material with different stress shape.

Constitutive Modeling for Elevated Temperature Flow Behavior of ZHMn34-2-2-1 Manganese Brass

The hot compressive deformation behaviors of ZHMn34-2-2-1 manganese brass are investigated on Thermecmastor-Z thermal simulator over wide processing domain of temperatures (923K-1073K) and strain rates (0.01s-1-10s-1). The true stress-strain curves exhibit a single peak stress, after which the stress monotonously decreases until a steady state stress occurs, indicating a typical dynamic recrystallization. A revised constitutive model coupling flow stress with strain, strain rate and deformation temperature is established with the material constants expressed by polynomial fitting of strain. Moreover, better prediction ability of the constitutive model is achieved by implementation of a simple approach for modified the Zener-Hollomon parameter considering the compensation of strain rate and temperature increment. By comparing the predicted and experimented values, the correlation coefficient and mean absolute relative error are 0.997 and 2.363%, respectively. The quantitative statistical results indicate that the proposed constitutive model can precisely characterize the hot deformation behavior of ZHMn34-2-2-1 manganese brass.