File Name: high temperature deformation and fracture of materials .zip
High temperature deformation behavior, especially the superplasticity of an Al-Li alloy, was studied within the recent framework of the internal variable theory of structural superplasticity. The effect of grain size was also examined by varying the grain sizes through a proper thermomechanical treatment.
The flow curves were found to be composite curves consisting of contributions from grain boundary sliding GBS and grain matrix deformation GMD at superplastic temperatures. The activation energy obtained for GMD was The high temperature deformation behavior, including superplasticity, of crystalline materials has generally been described phenomenologically by a power-law relation between the two external variables, namely, flow stress and strain rate , as follows [ 1 , 2 ]: where is a constant.
The strain rate sensitivity parameter, , can then be defined as the slope of the versus curves. This parameter has widely been used as one of the most important parameters characterizing the superplastic deformation behavior [ 1 — 3 ]. The value of is, however, observed to vary continuously along the versus curves, unable to provide a critical value above which superplastic deformation can be predicted [ 4 ].
When it comes to structural superplasticity SSP , it is apparent that the external or phenomenological variables such as , , and alone cannot adequately describe SSP. Superplasticity is a deformation process that produces large elongation of more than several hundred percent in crystalline materials, usually deformed in tension at a very low level of stress. Grain boundary sliding GBS is widely accepted as the most important deformation mechanism of superplasticity.
In general, superplastic properties are exhibited in materials having a stable, equiaxed, and extremely fine microstructure only under a very narrow range of strain rate and temperature normally above 0. A new approach to structural superplasticity SSP has been made by taking the dislocation glide mechanism as the major accommodation process for GBS [ 5 ], instead of the generally accepted high temperature diffusion process [ 6 ].
The justification for this approach comes from the observation that the superplastic deformation usually occurs in the strain rate range coinciding with that of plastic deformation caused by a dislocation glide. The load relaxation test provided the flow data in a much wider range of strain rate with minimal microstructural change or constant microstructure during the test [ 7 , 8 ], making it possible to analyze the flow curves within the framework of the internal variable theory of SSP.
The effect of grain size and temperature on the flow behavior of Al-Li alloy was specifically investigated based on the internal variable theory of SSP, and a critical condition for superplastic deformation is proposed. The next section provides a brief description of the internal variable theory of SSP.
The typical internal variable model, proposed by Chang and Aifantis [ 9 ], has described in detail a constitutive framework to consider inelastic deformation based on the notion of internal strain and internal spin tensors together with their precise micromechanical origin. Repeating here some important concepts of the model, a simple rheological model has been proposed by considering the grain matrix deformation GMD as a major accommodating process for GBS [ 5 ]. The two deformation mechanisms, that is, GBS and GMD, compete with each other in high temperature deformation of polycrystalline materials when it is not confined to SSP.
An elementary material volume bounded by the surface within and across which dislocations are allowed to move in response to a stress field is considered here. When the material boundary acts as a strong barrier partially blocking the passage of dislocations, some of dislocations would remain inside the material volume, giving rise to an internal strain , while at the same time the rest of the dislocations will pass through to produce an externally observable plastic deformation.
These simultaneous processes of accumulation within and the passage through of dislocations are believed to be the most fundamental deformation mechanism responsible for various mechanical phenomena, such as plasticity [ 10 ], phase transformation [ 11 ], and fracture.
Instead of using the phenomenological power law relation between and , a simple rheological model is used in this study. This model given in Figure 1 shows that GBS is mainly accommodated by a dislocation process, giving rise to an internal strain and plastic strain rate.
For the model given in Figure 1 , we derived the following stress relation and kinematic relation among the deformation rate variables, , , and , due to GBS:. The internal variables and represent the internal stress required to overcome a long-range interaction force among glide dislocations and the friction stress to surmount a short-range interaction force between dislocations and lattices, respectively.
The time rate denotes the materials time rate [ 12 ] of change of internal strain tensor similar to that prescribed by Hart [ 13 ]. A topological representation for this model is given in Figure 2. The constitutive relations between the stress variables and the deformation rate variables for grain matrix plastic deformation have been prescribed [ 5 ] in a form similar to that of Hart [ 13 ] from the viewpoint of simple dislocation kinetics.
These relations can be written as follows: where , , , and are the material constants. Equation 4 is, in fact, a kinetic rate equation of a mechanical activation process for a leading dislocation to overcome grain boundaries. Equation 6 represents the friction glide process of dislocations in lattice.
Considering the GBS as a viscous drag process similar to the frictional glide process of dislocations, the following power-law relation has been prescribed as [ 5 ] where and denote material constants. The constitutive parameters and are the static friction stress and its conjugate reference rate for GBS, respectively. We can, therefore, describe high temperature deformation behavior of crystalline materials with the constitutive relations for and elements.
The A1-Li alloy used in this study was supplied in the form of a plate with the thickness of A proper thermomechanical treatment TMT is required before expecting the superplasticity for this alloy, because the as-received material has elongated and pancake-shaped microstructure. The basic concept of thermomechanical treatment for grain refinement of precipitation hardening aluminum alloy proposed by Wert et al. All specimens after the recrystallization process were directly quenched into cold water.
The optical micrographs of thermomechanically treated specimens are given in Figure 3. In the load relaxation test employed in this study, a specimen was loaded first in tension to a certain predetermined extension value followed by stopping cross-head motion. The load was then recorded as a function of time at the fixed cross-head position.
The variation of the load was monitored through a digital voltmeter HP A DVM and stored in a personal computer for further processing. The flow stress and inelastic strain rate were then calculated from the load-time data following the usual procedure described in the literature [ 15 ]. All specimens were pulled to fracture at a constant cross-head speed. The values of constitutive parameters were determined by fitting the experimental data to 4 , and the results are presented in Table 2.
The solid lines in Figure 4 are the predicted curves representing the flow behavior of element described by 4 constructed with the constitutive parameters listed in Table 2. They show a good agreement with experimental data. It is clear from the figure that the specimens with such a large grain size reveal only the plastic deformation behavior of element regardless of test temperatures.
The solid lines in Figure 5 again represent the predicted curves from 4 constructed with the values of constitutive parameters listed in Table 3 , and they are also in good accord with the experimental data. The effect of raising temperature is manifested by the lower values of internal strength parameter as one can readily see in the tables. It is also interesting to note that the value of parameter characterizing dislocation permeability of strong barriers, that is, grain boundaries [ 9 ], was obtained as 0.
The value of this parameter is believed to strongly depend on the boundary properties, including its geometry and the properties of dislocations. From this point of view, it is necessary to examine the effect of variation in crystal structure on the value of this parameter, and interesting results have been obtained in Sn and Sn-containing alloys [ 5 , 10 ]. The value of in these alloys is 0.
In the case of load relaxation test employed in this study, total strain applied to a specimen is about , very small in every case. Therefore, the parameter depends strongly on the boundary characteristics. A more systematic research in this regard is needed including microstructure observation. As usually reported by other researchers, when the grain size was decreased and the initial strain rate lowered, the elongation clearly increased.
One of the most important features of the internal variable approach employed in this study is that each deformation mechanism of high temperature deformation, that is, GMD and GBS, can be considered individually.
By taking the difference between obtained directly from the relaxation test and estimated from 4 as the strain rate due to GBS, , according to 3 , the flow curves for GBS could be constructed as shown in Figure 8. The constitutive parameters required in 8 were then determined again by a nonlinear curve fitting method, and the results are given in Table 5.
The bold solid lines in Figure 8 represent the composite curves predicted by 3 , 4 , and 8 assuming , and they show a good agreement with the experimental data. The most significant result obtained by this analysis is that the GBS can, in fact, be described as a Newtonian viscous flow characterized by the power index value of , which can be confirmed experimentally by the work of Raj and Ashby [ 16 ]. As pointed out in an earlier work [ 5 ], they directly measured the sliding by loading helical springs wound of silver wire with a bamboo structure and found that the boundaries slide in a Newtonian viscous manner at high temperatures within a certain stress range.
Their result is very consistent with the analysis result of the present study, although the materials used in each study are very different.
Experimental data themselves in Figure 6 do not show a Newtonian viscous behavior at all. The situation where the flow curves were obtained is thought to be very similar to the latter case of the study of Raj and Ashby [ 16 ], and it is clear that the intragranular slip plays an important role in SSP. In the situation where GBS is fully accommodated, has been proved to be over 0. While several measurements [ 19 ] indicated very limited dislocation activity in region II, recent direct measurements of the intragranular strain in a superplastic Pb-Sn eutectic alloy have shown that the strain is oscillatory in nature, with both positive and negative components, and it makes no net contribution to the total elongation of the specimen [ 20 ].
This result is consistent with our discovery that the grains remain nearly equiaxed after superplastic deformation. Most of the determinations of in superplasticity experiments have relied upon the method proposed by Bell and Langdon [ 21 ].
We estimated value indirectly from Figure 6 to be about 0. Perevezentsev et al. The strain rate ranges for superplastic deformation due to GBS obtained in this study are also within these upper and lower bounds. The experimental results given in Figures 4 to 6 reveal the effect of temperature on the flow behavior of Al-Li alloy. As previously mentioned, the effect of raising temperature is seen to make the flow curves shift noticeably toward the lower stress and the higher strain rate region.
Figures 4 to 6 show that GBS is greatly affected by the test temperature. The value of the internal strength parameter decreases with the increase of temperature as in Tables 2 to 4. We believe that this is caused by a thermal softening effect which influences the mechanical properties of metals. The value of in 4 represents the hardness state, as it was first used by Ha et al.
As shown in Table 4 , in the temperature range within which the variation of is negligible, the effect of increase in temperature is to increase the value of reference strain rate , and so the flow curve shifts in the higher strain rate region.
This effect combined with the thermal softening makes the flow curves shift toward the higher strain rate and the lower stress region. From Figure 6 and Table 4 , it is possible to determine the activation energies for the high temperature deformation mechanisms employed in this study. However, only the activation energy for GMD element was obtainable due to the restrictions of experimental conditions and the difficulty in data analysis.
The activation energy can be determined from the following relation obtained by differentiating 5 :. Very similar results have been reported by Pu et al. This value was also found to be very similar to the activation energy of Al-3Li Figure 10 clearly shows the effect of GBS on the flow behavior of materials.
As seen in the tables, the value of internal strength parameter increases with the decrease of grain size regardless of temperatures. In the cases where GBS can operate as a major deformation process, however, the flow stress of the specimen with smaller grain size appears to be much lower than that of specimen with larger grain size. It seems rather reasonable to replace the flow stress in the classical Hall-Petch type relation with an internal structural variable since the grain size is also a structural variable representing the microstructure.
Very similar result has been obtained for Al alloy [ 28 ]. It can also be suggested that the superplastic deformation due to the GBS can only be observed under the following condition:.
To achieve this necessary condition for superplastic deformation caused by GBS, the temperature must be raised to reduce the static friction stress for GBS together with the increase in , which can be achieved through grain refinement according to the modified Hall-Petch relation given by By conducting a series of load relaxation and tensile tests on Al-Li alloy at high temperatures and by analyzing the results within the framework of the internal deformation variable theory, the following important results were obtained.
This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Journal overview.
Part 1 High temperature deformation: Creep behavior of materials; Evolution of dislocation substructures during creep; Dislocation motion at elevated temperatures; Recovery - creep theories of pure metals; Creep of solid solution alloys; Creep of second phase particles strengthened materials; Creep of particulates reinforced composite material; High temperature deformation of intermetallic compounds; Diffusional creep; Superplasticity; Mechanisms of grain boundary sliding; Multiaxial creep models. Part 2 High temperature fracture: Nucleation of creep cavity; Creep embrittlement by segregation of impurities; Diffusional growth of creep cavities; Cavity growth by coupled diffusion and creep; Constrained growth of creep cavities; Nucleation and growth of wedge - type microcracks; Creep crack growth; Creep damage mechanics; Creep damage physics; Prediction of creep rupture life; Creep - fatigue interaction; Prediction of creep - fatigue life; Environmental damage at high temperature. Du kanske gillar. Inbunden Engelska, Spara som favorit. Skickas inom vardagar.
High temperature strength is defined as the resistance of a material to high temperature deformation and fracture. This important book provides a valuable reference to the main theories of high temperature deformation and fracture and the ways they can be used to predict failure and service life. Analyses creep behaviour of materials, the evolution of dislocation substructures during creep, dislocation motion at elevated temperatures and importantly, recovery-creep theories of pure metals Examines high temperature fracture, including nucleation of creep cavity, diffusional growth and constrained growth of creep cavities A valuable reference to the main theories of high temperature deformation and fracture and the ways they can be used to predict failure and service life Download High Temperature Deformation and Fracture of Mater The benefit you get by reading this book will be information inside this e-book incredible fresh, you will get info which is getting deeper anyone read a lot of information you will get. This kind of High Temperature Deformation and Fracture of Materials Woodhead Publishing in Materials without we recognize teach the one who examining it become critical in imagining and analyzing. Don't become worry High Temperature Deformation and Fracture of Materials Woodhead Publishing in Materials can bring if you are and not make your handbag space or bookshelves' turn out to be full because you can have it in your lovely laptop even mobile phone. This High Temperature Deformation and Fracture of Materials Woodhead Publishing in Materials having fine arrangement in word and also layout, so you will not experience uninterested in reading.
Meanwhile, the phase and microstructure changes before and after deformation were investigated by X-ray diffractometer XRD , optical microscope OM , scanning electron microscopy SEM and transmission electron microscopy TEM. The results indicate that yield strength, tensile strength and elongation decrease with temperature increasing. The TWIP steel is single-phase of austenite before and after deformation. Analysis on the microstructure shows that the deformation twins gradually decrease with increasing temperature. The deformation process cannot benefit from the deformation twins, which is responsible for the decreased ductility.
Welding is an important joining method to fabricate the dissimilar welding integral blisk structure of single crystal and polycrystalline superalloy. The microstructure and properties of the welded joint are the key factors to determine the reliability of the integral blisk structure of dissimilar superalloys. The single crystal superalloy of DD and polycrystalline superalloy of IN were butt welded by continuous fiber laser system. The evolution of microstructure and composition segregation of the welded joints fabricated under the optimized welding parameters as-welded AW and after post weld heat treatment PWHT were investigated.
Progress in Nitrogen Ceramics pp Cite as. Three factors are currently hindering progress in adapting structural ceramics to high performance engineering practice: 1 variable strength, 2 lack of in-depth design practice, and 3 degradation of high temperature mechanical properties. The problem of strength variability is directly linked to fabrication and machining, both of which introduce the wide distribution of flaws and cracks responsible for failure. Directions to overcome this most important problem have been identified and within the next five years, one might expect significant progress on the commercial scale pending market applications. In-depth design practice requires experience which can only be gained, as it has in the last ten years, mainly by directed trial and error, i.
The energy, petrochemical, aerospace and other industries all require materials able to withstand high temperatures. High temperature strength is defined as the resistance of a material to high temperature deformation and fracture. This important book provides a valuable reference to the main theories of high temperature deformation and fracture and the ways they can be used to predict failure and service life.
In materials science , creep sometimes called cold flow is the tendency of a solid material to move slowly or deform permanently under the influence of persistent mechanical stresses. It can occur as a result of long-term exposure to high levels of stress that are still below the yield strength of the material. Creep is more severe in materials that are subjected to heat for long periods and generally increases as they near their melting point. The rate of deformation is a function of the material's properties, exposure time, exposure temperature and the applied structural load.
Meanwhile, the phase and microstructure changes before and after deformation were investigated by X-ray diffractometer XRD , optical microscope OM , scanning electron microscopy SEM and transmission electron microscopy TEM.