Strain Rate Sensitivity Coefficient Research Articles

Rate-Dependent Cohesive Zone Model for Fracture Simulation of Soda-Lime Glass Plate

In this paper, rate-dependent cohesive zone model was established to numerical simulate the fracture process of soda-lime glass under impact loading. Soda-lime glass is widely used in architecture and automobile industry due to its transparency. To improve the accuracy of fracture simulation of soda-lime glass under impact loading, strain rate effect was taken into consideration and a rate-dependent cohesive zone model was established. Tensile-shear mixed mode fracture was also taken account. The rate-dependent cohesive zone model was implemented in the commercial finite element code ABAQUS/Explicit with the user subroutine VUMAT. The fracture behavior of a monolithic glass plate impacted by a hemispherical impactor was simulated. The simulation results demonstrated that the rate-dependent cohesive zone model is more suitable to describe the impact failure characteristics of a monolithic glass plate, compared to cohesive zone model without consideration of strain rate. Moreover, the effect of the strain rate sensitivity coefficient C, the mesh size of glass plate and the impact velocity on the fracture characteristics were studied.

Formability of the 5754-Aluminum Alloy Deformed by a Modified Repetitive Corrugation and Straightening Process.

Sheets of 5754-aluminum alloy processed by a modified repetitive corrugation and straightening (RCS) process were tested in order to measure their formability. For this purpose, forming limit curves were derived. They showed that the material forming capacity decreased after being processed by RCS. However, they kept good formability in the initial stages of the RCS process. The formability study was complemented with microstructural analysis (derivation of texture) and mechanical tests to obtain the strain-rate sensitivity. The texture analysis was done by employing X-ray diffraction, obtaining pole figures, and the orientation distribution function. It was noticed that the initial texture was conserved after successive RCS passes, but the intensity dropped. RCS process did not induce β-fiber, contrary to common deformation process. The strain-rate sensitivity coefficient was measured through tensile tests at different temperatures and strain rates; the coefficient of the samples processed after one and two passes were still relatively high, indicating the capacity to delay necking, in agreement with the good formability observed in the initial passes of the RCS process.

Effect of ultrasonic pretreatment on the superplasticity of titanium alloy Ti-6Al-4V processed by ECAP

Improving the superplasticity characteristics of alloys widely used in industry, such as titanium alloy Ti-6Al-4V, is an important practical problem. Processing by the methods of severe plastic deformation can reduce the temperature of superplasticity. However, the material exhibits high flow stresses. In this work we studied the effect of preliminary ultrasonic treatment with an amplitude of oscillating tension-compression stresses of 100 MPa on the characteristics of superplasticity of the Ti-6Al-4V alloy processed by equal channel angular pressing (ECAP). It is shown that high-frequency oscillating stresses resulted in the reduction of the flow stress, the increase in elongation and the strain rate sensitivity coefficient during tensile tests in the conditions of superplasticity.

Hot tensile deformation and fracture behaviors of a typical ultrahigh strength steel

The hot tensile deformation and fracture behaviors of a typical ultrahigh strength steel are investigated by isothermal uniaxial tensile experiments over the tensile temperatures of 900–1150 °C and strain rates of 0.01–10 s-1. By combining the results of tensile tests and microstructural observation, the effects of deformation processing parameter (strain rate and tensile temperature) on the macroscopic plastic deformation behaviors, microscopic fracture morphologies and microstructural evolution are clarified. The studies indicate that the hot tensile behavior of the studied steel is greatly influenced by the competition of damage evolution, work hardening, and dynamic softening. With the increased strain rate, the strain rate sensitivity coefficients decrease, but the value of elongation to fracture increase from 0.38 to 0.50. The variations of microvoids or cracks in amounts and sizes show an increasing trend with the increased strain rate or the decreased tensile temperature. At the low tensile temperature (900 °C), the poor capability of necking diffusion hardly prevents the strain localization, and the mesoscopic damages easily take place. As the strain rate increases from 0.01 to 10 s-1, the neat fracture morphologies gradually change to the serrated. The main ductile fracture mechanisms transform from the intergranular fracture at the high tensile temperature and low strain rate to the transgranular fracture at the low tensile temperature and high strain rate.

Principles of achieving superior superplastic properties in intermetallic alloys based on γ-TiAl+α2-Ti3Al

Superplastic behavior of the Ti-43.7Al-4.2Nb-0.5Mo-0.2B-0.2C alloy (at. %) in a fine grained condition consisted of ultrafine grains and remnant lamellar colonies has been investigated. The fine grained condition was produced via two-stage hot forging with decreasing the forging temperature in the temperature range of T = 1200-950 °C. The produced material was used for preparation of specimens for tensile testing. The tensile tests were performed at T = 800–1000 °C and ε′∼10−4-10−3 s−1 in air without any protection against oxidation. The tests showed incredible superplastic elongations (δ = 1270–2860%) at T = 900–1000 °C and enhanced values of the strain rate sensitivity coefficient, m > 0.3 at ε′∼10−4-10−3 s−1. The obtained superplastic properties and microstructural examination of the tensile strained specimens suggest that the grain boundary sliding was the predominant deformation mechanism during superplastic flow. Superior superplastic properties were attained owing to unusually slow dynamic grain growth during superplastic flow. This was supported by a high content of the α2-Ti3Al phase, high alloying with niobium and dynamic recrystallization/globularization during superplastic flow leading to transformation of remnant lamellar colonies into the fine grains. The activation energy was defined as Q ≈310 kJ/mol suggesting that the predominant deformation mechanism during superplastic flow was grain boundary sliding controlled by volume diffusion of aluminum and titanium in γ-TiAl and α2-Ti3Al. On basis of the performed study, the principles of achieving superior superplastic properties (δ>1000%) in intermetallic alloys based on γ-TiAl+α2-Ti3Al have been proposed.

Effects of Temperature and Strain Rate on the Fracture Behaviors of an Al-Zn-Mg-Cu Alloy.

Effects of temperature and strain rate on the fracture behaviors of an Al-Zn-Mg-Cu alloy are investigated by isothermal uniaxial tensile experiments at a wide range of temperatures and strain rates, from room temperature (RT) to 400 °C and from 10−4 s−1 to 10−1 s–1, respectively. Generally, the elevation of temperature leads to the increasing of elongation to fracture and the reduction of peak stress, while higher strain rate results in the decreasing of elongation to fracture and the increasing of peak stress. Interestingly, we found that the coefficient of strain rate sensitivity (m-value) considerably rises at 200 °C and work of fracture (Wf) fluctuates drastically with the increase of strain rate at RT and 100 °C, both of which signify a non-uniform and unstable deformation state below 200 °C. A competition of work hardening (WH) and dynamic recrystallization (DRX) exists at 200 °C, making it serve as a transitional temperature. Below 200 °C, WH is the main deformation mechanism of flow stress, and DRX dominates the flow stress above 200 °C. It has been found that from RT to 200 °C, the main feature of microstructure is the generation of dimples and microvoids. Above 200 °C, the coalescence of dimples and microvoids mainly leads to the failure of specimen, while the phenomenon of typically equiaxed dimples and nucleation appear at 400 °C. The observations of microstructure are perfectly consistent with the related macroscopic results. The present work is able to provide a comprehensive understanding of flow stress of an Al-Zn-Mg-Cu alloy at a wide range of temperatures and strain rates, which will offer valuable information to the optimization of the hot forming process and structural design of the studied alloy.

Tensile Deformation Behaviors of Aluminum Alloy 2219 at High Temperatures from 415°C to 515°C

This study is carried out to provide detailed hot deformation information on aluminum alloy AA2219-O. The uniaxial tensile tests are carried out to study the hot deformation behaviors. The test temperature ranges from 415°C to 515°C, and the strain rates are 0.001s-1 and 0.01s-1. Additionally, the analysis of the strain rate sensitivity coefficient indicates that the AA2219-O exhibits the trend of superplasticity at temperatures above 475°C.

Effect of Ultrasonic Treatment on the Characteristics of Superplasticity of Titanium Alloy Ti-6Al-4V

Effect of ultrasonic treatment (UST) with an amplitude of oscillating tension-compression stresses 100 MPa on the characteristics of superplastic deformation of Ti-6Al-4V alloy with an ultrafine grained (UFG) structure processed by equal-channel angular pressing (ECAP) is studied. During tensile tests at 600°C with initial strain rates in the interval from 10-4 to 10-3 s-1, ultrasonically irradiated samples exhibit a reduced flow stress, higher values of the strain rate sensitivity coefficient and elongation to failure as compared to the samples tested directly after ECAP. Detailed studies of the microstructure of samples subjected to ECAP only and ECAP followed by UST revealed no considerable differences. It is suggested that the UST affected fine structure of the material bringing them to a state with a higher ability of relaxation of deformation-induced defects.

An isothermal forming process with multi-stage variable speed for magnesium component assisted by sensitivity analysis

We have developed a multi-stage variable speed (MSV) isothermal forming process based on strain rate sensitivity (SRS) analysis, and successfully produced a large size of rib-web component of magnesium alloy from a cylindrical billet. The obtained rib-web component has been processed into parts for mechanical properties examination and the examination results met the standard of being safely used in aircrafts. The process parameters of the forming technology and microstructure change were explicitly linked by the SRS coefficient. The finite element (FE) simulation and SRS distribution were implemented to identify the relationship among process parameters, shaping characteristics, and microstructure development. The MSV speed process was employed for reducing the forming load, refining grain sizes and increasing the strength of the component. With the selected process parameters the maximum forming load was reduced to be less than 20 MN, which is 55.3% lower than that used in the same process with the initial constant speed unchanged. Fine dynamic recrystallization (DRX) were observed from all parts of the forged cover plate including the convex, ribs, and web region. It was also found that higher strain resulted in more uniform distribution of fine β-Mg17Al12 precipitates and larger DRX volume fraction. Importantly the developed isothermal forming process with severe plastic deformation can be applied for obtaining grain refinement so improving the mechanical properties of Mg products.

Superplastic Deformation Behavior of Multi‐Pass Warm Rolled Ti–6Al–4V Titanium Alloy at Low Temperature and High Strain Rate

The superplastic deformation behavior of Ti–6Al–4V alloy is investigated by the tensile tests for multi‐pass warm rolled Ti–6Al–4V alloy at temperature of 700–870 °C and strain rate of 10−3–10−2 s−1. A maximum elongation of 1550% is obtained at temperature of 800 °C and strain rate of 10−3 s−1. Even at the low temperature of 700 °C and the high strain rate of 10−2 s−1, the elongation is still 356%. The enhanced superplasticity at low temperature and high strain rate is due to the refined microstructure with fragmented and uniformly distributed fine β grains and to the high density dislocation around grain boundaries as well as dynamic recrystallization. The activation energy at temperature of 800 and 870 °C is 226.8 and 220.2 kJ mol−1, but it increases to 377.5 kJ mol−1 at temperature of 700 °C. The average activation energy is 274.8 kJ mol−1 suggesting that the predominant deformation mechanism is grain boundary sliding. The coefficient of strain rate sensitivity increases with the temperature.

Effect of Various SPD Techniques on Structure and Superplastic Deformation of Two Phase MgLiAl Alloy

MgLiAl alloy containing 9 wt% Li and 1.5% Al composed of hexagonal α and bcc β phases was cast under protecting atmosphere and hot extruded. Various methods of severe plastic deformation were applied to study their effect on structure and grain refinement. Rods were subjected to 1–3 passes of Twist Channel Angular Pressing TCAP (with helical component), cyclic compression to total strain e = 5 using MAXStrain Gleeble equipment, both performed at temperature interval 160–200 °C and, as third SPD method, KOBO type extrusion at RT. The TCAP pass resulted in grain refinement of α phase from 30 μm down to about 2 μm and that of β phase from 12 to 5 μm. Maxstrain cycling 10 × up to e = 5 led to much finer grain size of 300 nm. KOBO method performed at RT caused average grain size refinement of α and β phases down to about 1 μm. Hardness of alloy decreased slightly with increasing number of TCAP passes due to increase of small void density. It was higher after MAXStrain cycling and after KOBO extrusion. TEM studies after TCAP passes showed higher dislocation density in the β region than in the α phase. Crystallographic relationship (001) α|| (110) β indicated parallel positioning of slip planes of both phases. Electron diffraction technique confirmed increase of grain misorientation with number of TCAP passes. Stress/strain curves recorded at temperature 200 °C showed superplastic forming after 1st and 3rd TCAP passes with better superplastic properties due to higher elongation with increasing number of passes. Values of strain rate sensitivity coefficient m were calculated at 0.29 after 3rd TCAP pass for strain rate range 10−5 to 5 × 10−3 s−1. Deformation by MAXStrain cycling caused much more effective grain refinement with fine microtwins in α phase. Superplastic deformation was also observed in alloy deformed by KOBO method, however the value of m = 0.21 was obtained at lower temperature of deformation equal to 160 °C and deformation rate in the range 10−5 to 5 × 10−3. Tensile samples deformed superplastically showed grain growth and void formation caused by grain boundary slip. Summarizing, all methods applied resulted in sufficient grain refinement to obtain the effect of superplastic deformation for alloys of two phase α + β structure.

Dynamic Behavior of AA2519-T8 Aluminum Alloy Under High Strain Rate Loading in Compression

In this study, the effects of strain rate on the dynamic behavior, microstructure evolution and hence, failure of the AA2519-T8 aluminum alloy were investigated under compression at strain rates ranging from 1000 to 3500 s−1. Cylindrical specimens of dimensions 3.3 mm × 3.3 mm (L/D = 1) were tested using the split-Hopkinson pressure bar integrated with a digital image correlation system. The microstructure of the alloy was assessed using optical and scanning electron microscopes. Results showed that the dynamic yield strength of the alloy is strain rate dependent, with the maximum yield strength attained by the material being 500 MPa. The peak flow stress of 562 MPa was attained by the material at 3500 s−1. The alloy also showed a significant rate of strain hardening that is typical of other Al–Cu alloys; the rate of strain hardening, however, decreased with increase in strain rate. It was determined that the strain rate sensitivity coefficient of the alloy within the range of high strain rates used in this study is approximately 0.05 at 0.12 plastic strain; a more significant value than what was reported in literature under quasi-static loading. Micrographs obtained showed potential sites for the evolution of adiabatic shear band at 3500 s−1, with a characteristic circular-shaped surface profile comprising partially dissolved second phase particles in the continuous phase across the incident plane of the deformed specimen. The regions surrounding the site showed little or no change in the size of particles. However, the constituent coarse particles were observed as agglomerations of fractured pieces, thus having a shape factor different from those contained in the as-received alloy. Since the investigated alloy is a choice material for military application where it can be exposed to massive deformation at high strain rates, this study provides information on its microstructural and mechanical responses to such extreme loading condition.

Об испытании сплошных цилиндрических образцов при растяжении с кручением

One of the features of the rheological behavior of metals and alloys at high temperature is their sensitivity to the rate of deformation. This paper proposes a method for studying the dependence between stresses and strain rates based on experimental data for solid cylinder specimen deformed in tension with torsion under non-proportional deformation (complex loading). A strain trajectories with two straight lines is considered. The deformation process is described by two components of the strain rate tensor (axial and shear) in the form of functions of time. At each time, we record the axial force and torque corresponding to them. The function of the force parameters (axial force and torque) recorded in the experiment and the preset kinematic parameters (the rate of tension and the torsional velocity), the strain rate sensitivity coefficient, the strain hardening exponent and the approach angle between the stress vectors and the strain rate on the specimen surface under non-proportional deformation is obtained. The paper also considers particular cases of deformation trajectories of the double-link type, when the second link is uniaxial tension, pure torsion or tension combined with torsion. Analytic formulas for calculating the stress vector and its components, and the approach angle that characterizes the direction of the stress vector in relation to the strain rate vector for points on the specimen cylindrical surface are derived. The method proposed is a generalization of the experimental procedure for plotting shear diagrams from the torsion test data for a material sensitive to the rate and level of strains, based on the Fields Backofen equation. The proposed method was used in processing experimental data obtained after testing the Ti-6Al-4V titanium alloy under non-proportional deformation in tension with torsion under conditions of superplasticity. When processing the test data, the compliance of the “specimen – testing machine” system was taken into account.

SUPERPLASTIC DEFORMATION OF TWO PHASE MgLiAl ALLOY AFTER TCAP PRESSING

Magnesium based alloy containing 9 wt. % Li, 1,5 wt. % Al, composed of  (hcp + bcc) phases was cast under argon atmosphere and extruded at 350oC as bars of cross section 12x12 mm. Twist Channel Angular Pressing TCAP deformation was applied at a temperature of 160oC using BC rotation of samples in the following passes. TCAP tool consisted of helical part in horizontal area of the channel with an angle of lead γ = 30° to simulate back pressure and thus to increase the extrusion force. The initial grain size of the hexagonal  phase estimated at 30 m decreased in the following passes down to 6 m and that of bcc  phase decreased after TCAP from initial 12 m, down to 5 m. TEM studies after TCAP passes showed higher dislocation density in the  region than in the  phase. Crystallographic relationship (001)  || (110)  indicates parallel positioning of slip planes of both phases due to activation of slip. Electron diffraction indicates increase of grain misorientation with a number of TCAP passes. Stress/strain curves measured at temperature of 200oC show superplastic forming after 1st and 3rd TCAP passes with better superplastic properties with increasing number of passes. Values of strain rate sensitivity coefficient m were calculated at 0.31 after 1 TCAP pass using flow stress values from step strain increase curves. The sample after 3 TCAP passes showed increase of m value up to 0.47 for the strain rate range 10-5 – 5 x 10-4 s-1. Obtained values are slightly lower than those reported in the literature, however increase of a number of TCAP passes has a positive effect on superplastic properties due to fine grains and increase of their misorientation.

The Effect of Al on the Mechanical Properties and Microstructure of Copper-based Metallic Glass

An investigation was carried out into the effect of different amounts of Al on the mechanical properties, and glass-forming ability, of a three component alloy (Cu–Zr–Al). The mechanical properties were studied using a universal materials tester and a Split-Hopkinson bar tester. A series of amorphous alloys with different Al content were subjected to static compression and dynamic high-speed impact tests at 10−1 s−1, 10−2 s−1, and 10−3 s−1 for the static condition and 2000 s−1, 3000 s−1, and 4000 s−1 for the dynamic condition. Experiment showed that the flow stress value and the strain rate sensitivity coefficient of the copper-based amorphous alloys varied with changes of strain and strain rate. An increase in the rate of strain caused the flow stress value and the sensitivity coefficient of the strain rate to rise. When the Al content in an amorphous alloy Cu47.5Zr45.5Al7 was 7%, both the flow stress value and the strain were improved and effectively upgraded the mechanical properties of the material.

The same strain-rate sensitivity coefficient of 1/6 demonstrated from DRX critical and steady state during hot deformation for metallic materials

Metal forming and shaping is becoming advanced and their processing is becoming modelled gradually. Arrhenius constitutive models for critical and steady state when dynamic recrystallization (DRX) for metallic materials have been constructed from internal variables. Isothermal compression on two typical metallic materials were conducted for verification. Stress of DRX critical and steady state was identified through flow curves according to Poliak-Jonas and their microstructure. The linear relationship between critical and steady stress during hot deformation has been validated.

Strain-rate sensitivity of powder metallurgy superalloys associated with steady-state DRX during hot compression process

Strain-rate sensitivity (SRS) is an important parameter to describe the thermodynamic behavior in plastic deformation process. In this research, the variation of SRS associated with steady-state DRX in P/M superalloys was quantitatively investigated. Based on the theoretical analysis and microstructural observation of the alloy after deformation, the SRS coefficient was employed to identify the deformation mechanism of the alloy. Meanwhile, the corresponding relationship between SRS coefficient m, stress exponent n and deformation mechanism was revealed. The stress exponent n in the Arrhenius constitutive model of P/M superalloys was calculated. In addition, it is found there is a relatively stable stress exponent range (n = 4-6), indicating that dislocation evolution played as the major hot deformation mechanism for P/M FGH4096 superalloy. Furthermore, the Bergstrom model and Senkov model were used and combined together to estimate the SRS coefficient in the steady-state DRX and the m value maintains at 0.2-0.22, which are consistent with the microstructural evolution during hot deformation process. The SRS coefficient distribution map and power dissipation efficiency distribution map were finally constructed associated with the microstructural evolution during hot deformation, which can be used to optimize the processing parameters of the superalloys.

Hot deformation characteristics of AZ80 magnesium alloy: Work hardening effect and processing parameter sensitivities

Isothermal compression experiment of AZ80 magnesium alloy was conducted by Gleeble thermo-mechanical simulator in order to quantitatively investigate the work hardening (WH), strain rate sensitivity (SRS) and temperature sensitivity (TS) during hot processing of magnesium alloys. The WH, SRS and TS were described by Zener-Hollomon parameter (Z) coupling of deformation parameters. The relationships between WH rate and true strain as well as true stress were derived from Kocks-Mecking dislocation model and validated by our measurement data. The slope defined through the linear relationship of WH rate and true stress was only related to the annihilation coefficient Ω. Obvious WH behavior could be exhibited at a higher Z condition. Furthermore, we have identified the correlation between the microstructural evolution including β-Mg17Al12 precipitation and the SRS and TS variations. Intensive dynamic recrystallization and homogeneous distribution of β-Mg17Al12 precipitates resulted in greater SRS coefficient at higher temperature. The deformation heat effect and β-Mg17Al12 precipitate content can be regarded as the major factors determining the TS behavior. At low Z condition, the SRS becomes stronger, in contrast to the variation of TS. The optimum hot processing window was validated based on the established SRS and TS values distribution maps for AZ80 magnesium alloy.

Применение обратного анализа для определения реологических констант материалов по результатам тестовых формовок круглых мембран

The paper is devoted to a problem of determining rheological characteristics of materials from the results of experiments on free forming of sheet blanks to a cylindrical matrix. This information on the material behavior is used in the design of gas forming processes for the production of parts for aerospace industry. Realization of such technologies requires to follow optimum technological regimes, in computer simulations of which one should adequately describe the properties of materials under consideration. A significant disadvantage of the classical experimental method of tensile testing of plate specimens is that an information taken from these tests is related to metal forming in the conditions of uniaxial tension that is not typical for gas forming processes. Experimental method of forming circular membranes considered here allows one to study the behavior of a material in the conditions of biaxial tension. Interpretation of the results is proposed to carry out by an inverse analysis utilizing a special semianalytical model for the solution of the direct task. The key role in this semianalytical model belongs to a dependence of the blank thickness at the dome pole on the dome height, which accounts for the strain rate sensitivity coefficient. This approach was applied for the processing of experimental results obtained by free forming of industrial aluminum alloys. The material characteristics obtained were compared to charecteristics determined by other methods for the same set of experimental data available in the literature. To estimate the efficiency of the method proposed, the characteristics obtained were verified by finite element simulations. For simulations, MSC Nastran software was used. The results of the simulations were found to be in good agreement with the experimental data not only with respect to the dome height but also to the blank thickness at the dome.

The loading-rate dependent tensile behavior of CNT film and its bismaleimide composite film

Carbon nanotube (CNT) macroscopic assembly, as a promising candidate for the protective and anti-collision materials, has attracted lots of researchers to explore its mechanical behavior under different loading rates. In this paper, the loading-rate dependent mechanical behavior of CNT film and its composite with bismaleimide (BMI) matrix is investigated. The pristine CNT film shows decreased tensile strength by 33.8% when the loading rate increases from 0.05mm/min to 40mm/min. An obvious necking extending phenomenon is observed in the CNT film during the tensile test under lower tensile rates, e.g. 0.05mm/min and 0.5mm/min. However, the random composite film and the oriented composite film both display increased tensile strength, by 58.2% and 35.7% respectively, with the increasing loading rate from 0.05mm/min to 40mm/min. The different loading-rate dependence of tensile behavior is ascribed to the different tensile-induced motions of CNTs and CNT bundles in composite film. Moreover, strain rate sensitivity coefficients of different film are calculated according to a simplified Johnson-Cook model. The results suggest that the pristine CNT film with the strain rate sensitivity coefficient of −0.0941 has a high loading-rate sensitivity, meanwhile polymer infiltration and oriented alignment can weaken the loading-rate sensitivity of CNT film.