Internal Stress Superplasticity Research Articles

Experimental Observation of a New Attenuation Mechanism in hcp‐Metals That May Operate in the Earth's Inner Core

AbstractSeismic observations show the Earth's inner core has significant and unexplained variation in seismic attenuation with position, depth and direction. Interpreting these observations is difficult without knowledge of the visco‐ or anelastic dissipation processes active in iron under inner core conditions. Here, a previously unconsidered attenuation mechanism is observed in zinc, a low pressure analog of hcp‐iron, during small strain sinusoidal deformation experiments. The experiments were performed in a deformation‐DIA combined with X‐radiography, at seismic frequencies (∼0.003–0.1 Hz), high pressure and temperatures up to ∼80% of melting temperature. Significant dissipation (0.077 ≤ Q−1(ω) ≤ 0.488) is observed along with frequency dependent softening of zinc's Young's modulus and an extremely small activation energy for creep (⩽7 kJ mol−1). In addition, during sinusoidal deformation the original microstructure is replaced by one with a reduced dislocation density and small, uniform, grain size. This combination of behavior collectively reflects a mode of deformation called “internal stress superplasticity”; this deformation mechanism is unique to anisotropic materials and activated by cyclic loading generating large internal stresses. Here we observe a new form of internal stress superplasticity, which we name as “elastic strain mismatch superplasticity.” In it the large stresses are caused by the compressional anisotropy. If this mechanism is also active in hcp‐iron and the Earth's inner‐core it will be a contributor to inner‐core observed seismic attenuation and constrain the maximum inner‐core grain‐size to ≲10 km.

A composite model description of internal stress superplasticity

A simple two component composite model, each component having a different coefficient of thermal expansion, is used to describe internal stress superplasticity due to temperature cycling. The model adopts a creep rather than a plasticity approach and uses a single equation set to describe accelerated creep and the transition to normal creep behaviour at higher applied stresses. This is in contrast to some other descriptions where a separate equation is required for each type of behaviour and average values for material properties such as diffusion coefficients are used. The numerical solution makes the proposed method readily applicable to design situations, since actual temperature cycles can be taken into account. Results from the model are compared to previously published experimental work on zinc and results obtained during the present investigation.

Enhanced Foaming of Cellular Metals by Internal Stress Superplasticity

Enhanced Foaming of Cellular Metals by Internal Stress Superplasticity

Internal stress superplasticity in the NiAl–Mo eutectic alloy

Internal stress superplasticity (ISS) in a NiAl–Mo based eutectic alloy was investigated by conducting thermal cycling creep tests. The alloy was annealed at high temperatures to spheroidize the refractory metal phase. Under thermal cycling creep conditions, the alloy exhibited characteristics of ISS, that is, at low stresses, the thermal cycling creep rates were much higher than the isothermal creep rates and the corresponding stress exponent was close to 1. These results were compared quantitatively with the predictions of a theoretical model of ISS. The experimental thermal cycling creep rates agreed with the predicted values within an error less than one order of magnitude. Superplastic elongation of >200% without fracture was attained during a thermal cycling tensile creep test.

Thermal cycling creep behavior of NiAl–Cr alloy

Isothermal and thermal cycling creep behavior of a NiAl–Cr alloy was studied by compression tests. At low stresses, the thermal cycling creep rates were faster than the isothermal creep rates. The corresponding stress exponent under the thermal cycling condition was close to one. At high stresses, the stress exponent and the creep rate under the thermal cycling condition approached the isothermal values. The result indicates the occurrence of internal stress superplasticity at low stresses. The origin of internal stress was attributed to the difference in thermal expansion behavior of the constituent phases. Further, the thermal cycling creep rate was found to increase with increase in temperature amplitude and heating/cooling rate. The above trends were compared with the predictions of an internal stress superplasticity model. Good formability of the alloy under the thermal cycling condition was demonstrated through carrying out the thermal cycling compressive creep test to a large strain level.

Hydrogen-induced internal-stress plasticity in titanium

Internal-stress plasticity is a deformation mechanism resulting from the biasing of internal mismatch stresses by an external stress.[1] These internal stresses can be produced by a temperature change in materials with grains (or phases) exhibiting different thermal expansion coefficient[2] or different density during a phase transformation[3]; alternate sources of internal stresses include compressibility mismatch during pressure changes[4] and swelling mismatch during irradiation.[5] The most common type of mismatch generation is thermal, as it easily lends itself to cycling during which tensile strains well in excess of 100 pct can be accumulated; this phenomenon is known as internal-stress superplasticity.[1] The purpose of the present article is to report, for the first Fig. 1—Titanium-hydrogen phase diagram[14] showing chemical cycles time, internal-stress plasticity where internal stresses are used in the present study of chemically induced internal-stress plasticity induced by a reversible change of chemical composition (at at 805 or 860 8C ( pH2 5 0 } 4.1 kPa) as well as typical thermal cycles constant temperature and pressure) rather than a change used in the literature for thermally induced internal-stress plasticity in of temperature or pressure (at constant composition), as hydrogen-free Ti (T 5 860 } 900 8C). illustrated in Figure 1. We use the Ti-H system to demonstrate this effect, because hydrogen diffuses rapidly in and out of titanium where it produces mismatch strains both directly (by lattice swelling in the presence of concentration gradients) and indirectly (by inducing the hcp (a-Ti) to bcc (b-Ti) transformation), as demonstrated in a recent study of hydrogen-induced ratchetting.[6] We note that this chemically induced internal-stress plasticity is fundamentally different from thermochemical processing of titanium[7] where hydrogen alloying is used to produce a weaker, more easily workable b-Ti phase, and where internal stresses are unimportant. Titanium plates (99.7 pct pure, from Alpha Aesar, MA) were machined into dog-bone specimens with a gage 28 to 52 mm in length, 5.4 to 6.0 mm in width, and 2 mm in thickness. Specimens were tested in a low-stress creep apparatus described earlier,[8] modified to allow for a gas atmosphere flowing at a rate of 1.22 L/min, which could be changed from Ar (99.999 pct pure) to an Ar/4 vol pct H2 mixture. This 4.1 kPa hydrogen partial pressure corresponds to an equilibrium hydrogen concentration in titanium well within the b-Ti field (Figure 1). The specimen strain was continuously measured at the cold end of the load train and the temperature was maintained at a constant value of 805 8C 6 2 8C or 860 8C 6 2 8C by a thermocouple contacting the gage section or the pull head. Figure 2 shows the creep rate as a function of the applied Fig. 2—Isothermal creep rate at 805 8C and 860 8C for hydrogen-free astress for hydrogen-free a-Ti and for fully hydrogenated bTi and fully hydrogenated b-Ti. Ti at temperatures of 805 8C and 860 8C. The stress exponents

Internal stress superplasticity in anisotropic polycrystalline materials

A theoretical model of internal stress superplasticity is developed in a single-phase polycrystalline material with an anisotropic thermal expansion. Quasi-steady-state creep equation during a thermal cycle is derived quantitatively based on continuum micromechanics. The model assumes that the generated mismatch strain is accommodated simultaneously by the plastic flow of the material. The linear creep deformation, which corresponds to internal stress superplasticity, is obtained at low applied stress region, and the creep rate depends on the crystallographic texture of the material. The validity of the model is experimentally verified using polycrystalline zinc which is a typical metal having large anisotropy in thermal expansion. The calculated strain rates using the texture information and the isothermal creep equation agree quantitatively well with the experimental results. The apparent activation energy of thermal cycling creep reveals 1/ n ( n: stress exponent of isothermal creep) of that of isothermal creep, which is one of the characteristics of internal stress superplasticity. Except for the factors attributable to the material geometry, the thermal cycling creep equation in the polycrystalline material is identical to that in a metal matrix composite.

Internal Stress Superplasticity in a In-Situ Intermetallic Matrix Composite

Processing of NiAl-Cr based eutectic in-situ composite via internal stress superplasticity has been explored. The alloy is heat treated to produce spherodized Cr particles in NiAl matrix. Results of thermal cycling creep experiments indicate that internal stress of considerable magnitude are generated between the NiAl matrix and Cr particles, which aids the external applied stress in deforming the alloy in viscous manner The origin of internal stress is attributed to the difference in thermal expansion behavior of the constituent phases. At low stresses, the thermal cycling creep rates are higher than the isothermal creep rates. However, the observed thermal cycling creep rates are an order of magnitude lower than values predicted by an internal stress superplasticity model based on micromechanics. The possible reasons for this discrepancy are discussed.

Unified interpretation of internal stress superplasticity models based on thermally- activated kinetics

Three main theoretical models of internal stress superplasticity proposed by Greenwood and Johnson [ Proc. R. Soc. A, 1965, 283, 403], Sherby et al. [ Mater. Sci. Technol., 1985, 1, 925], and Sato and Kuribayashi [ Acta metall. mater., 1993, 41, 1759] have been expanded to include the temperature dependence of the average strain rate. It is revealed that the constitutive equations of these models are equivalent regarding the thermally activated kinetics, and that the apparent activation energy of internal stress superplasticity is equal to 1/ n (where n is the stress exponent of isothermal power-law creep) times that of isothermal power-law creep. This theoretical prediction has been experimentally verified by the thermal cycling creep tests using the same temperature profiles with several equivalent temperatures in a Be particle-dispersed Al matrix composite. The obtained apparent activation energy was 22 kJ/mol, which is approximately 1/7 times that of isothermal creep.

Mechanism of Internal Stress Superplasticity Based on Thermally-Activated Kinetics

Three main theoretical models for internal stress superplasticity (Greenwood and Johnson, Sherby et al., and Sato and Kuribayashi) were reexamined with respect to the temperature profile of the thermal cycling. Assuming a mismatch strain rate obeying a power-law, we concluded that three constitutive equations were essentially identical except for constant terms. It is predicted that the apparent activation energy of internal stress superplasticity is equal to 1/n (n: stress exponent of isothermal power-law creep) times that of isothermal power-law creep. This theoretical prediction has been experimentally verified by the thermal cycling creep tests using the same temperature profiles with several equivalent temperatures in At-Be eutectic composite.

Effects of Crystallographic Texture on Internal Stress Superplasticity Induced by Anisotropic Thermal Expansion

AbstractPolycrystalline materials having crystallographic anisotropy show internal stress superplasticity under thermal cycling conditions. The deformation mechanism is analyzed using a theoretical model based on continuum micromechanics including the effects of crystallographic texture. The model is experimentally verified through the thermal cycling creep tests using polycrystalline zinc having two kinds of fiber-texture, and agrees well with the experimental results.

Internal stress superplasticity in directionally solidified Al–Al 3Ni eutectic composite

Thermal cycling creep behavior in fiber-reinforced composites was investigated using a directionally solidified Al–Al 3Ni eutectic composite. A superplastic elongation of 120% was obtained during a thermal cycling tensile creep test. Compression creep tests were performed under an external stress applied either parallel or perpendicular to the growth direction. The average strain rates for the two directions exhibited the characteristics of internal stress superplasticity: those at low stresses were much higher than the corresponding isothermal creep rates and were proportional to the applied stress. In the case of transverse loading, the thermal cycling creep rate was explained quantitatively using the previously reported internal stress superplasticity model for particle-dispersed composite. In the case of longitudinal loading, it was much lower than that predicted using the model because of the difference in the stress state and the relaxation process. However, thermal cycling creep had very low activation energy, which is a unique characteristic of internal stress superplasticity.

Internal stress superplasticity in Al–Be eutectic alloy during triangular temperature profile

Materials containing second phases show superplastic behavior during thermal cycling (internal stress superplasticity). In the present study, this behavior has been investigated by thermal cycling creep tests with a triangular wave having fixed heating and cooling rates, using a Be-particle–dispersed Al matrix alloy. The thermal cycling creep rates were much higher than the isothermal creep rates and proportional to the applied stress at intermediate stresses. It was interpreted by the previous theoretical model of internal stress superplasticity, and the values of the thermal cycling creep rate were about 60% of the theoretical one. The discrepancy was explained by the transition after each temperature reversal until achieving the quasi-steady state stress distribution during thermal cycling.

A non-linear model for internal stress superplasticity

Most models of internal stress superplasticity predict a linear relationship between the applied stress and the plastic strain per cycle, and are only valid at low applied stresses. In the present paper, we extend the original linear theory of phase transformation superplasticity by Greenwood and Johnson [1] and derive a non-linear closed-form solution valid over the whole range of stresses, from the low-stress regime (where a linear relationship between strain and stress is predicted in agreement with the model by Greenwood and Johnson ( Proc. R. Soc. Lond., 1965, 283, 403), to the high-stress regime (where the strain increases non-linearly as the applied stress approaches the yield stress of the weaker phase). The model is found to be in agreement with literature data on transformation superplasticity of iron spanning both stress regimes. Furthermore, the model is adapted to the case where internal stresses are produced by thermal expansion mismatch: it is compared to experimental literature data for metals with anisotropic thermal expansion (Zn and U) and for metal matrix composites with inhomogeneous thermal expansion (Al SiC).

Micromechanical Analysis of Internal Stress Superplasticity Aiming at Single Crystal Superplastic Forming

Micromechanical Analysis of Internal Stress Superplasticity Aiming at Single Crystal Superplastic Forming

Al-Be共晶合金を用いた内部応力超塑性モデルの検証

Materials containing second phases show superplastic behavior during thermal cycling (internal stress superplasticity). The authors recently proposed a quantitative model using continuum micromechanics theory for the superplastic behavior. In the present study, this theoretical model has been verified by compression creep tests under thermal cycling conditions using a Be particle dispersed Al matrix alloy as an ideal material. The thermal cycling creep rates were much higher than the isothermal creep rates and proportional to the applied stress at low stresses. However they approached the isothermal creep rates at high stresses. This behavior agrees well with a theoretical prediction, and the value of the thermal cycling creep rate at low stresses coincides with the theoretical one. Therefore it was concluded that the internal stress superplasticity model was applicable to particle dispersed metal matrix composites.

Internal Stress Superplasticity Induced by Thermal Cycling in Metal Matrix Composite

Thermal cycling creep behavior of Al–Al3Ni eutectic alloy was studied by compression creep test. Three kinds of eutectic alloys were prepared; as-extruded alloy having polycrystal matrix and spherical Al3Ni phase, directionally solidified at 5 mm/h alloy having a single crystal matrix with short spheroidal Al3Ni phase, directionally solidified at 60 mm/h alloy having a single crystal matrix with long rod shaped Al3Ni phase. The strain rates of all specimens under thermal cycling conditions at low stresses were faster than the corresponding isothermal creep rates. However there is no significant difference at high stresses. The material having short spheroidal Al3Ni phase in the single crystal Al matrix had the lowest stress exponent (n=1) in thermal cycling creep at intermediate stresses, which is typical of superplastic behavior induced by internal stress, caused by a difference of thermal expansion between the matrix and inclusions.

On the Mechanism of Internal Stress Superplasticity

On the Mechanism of Internal Stress Superplasticity

A model of internal stress superplasticity based on continuum micromechanics

A new theoretical model is proposed to explain internal stress superplasticity under a simultaneous applied stress during thermal cycling. The analyzed material is an elasticity uniform body containing an elastic spherical inclusion, surrounded by a plastic matrix obeying a power law creep. It is assumed that only relaxation by interface diffusion is significant. At first it is shown that an inclusion dilatation can be counterbalanced by a certain matrix plastic flow. Assuming a certain stress distribution for this condition, a stationary flow on heating or cooling results. Typical behavior of this stationary flow is analyzed for the specific cases of high or low applied stresses. Under a low applied stress, the internal stress by an inclusion dilatation strongly accelerates the flow in the direction of the applied stress, which is in proportion to the applied stress, to the heating or cooling rate and to the inclusion volume fraction.

The influence of microstructure on internal stress superplasticity in polycrystalline zinc

The influence of microstructure on internal stress superplasticity in polycrystalline zinc