Deformation-mechanism diagrams

This competition between mechanisms is conveniently summarised on Deformation Mechanism Diagrams (Figs. 19.5 and 19.6). They show the range of stress and temperature (Fig. 19.5) or of strain-rate and stress (Fig. 19.6) in which we expect to find each sort of creep (they also show where plastic yielding occurs, and where deformation is simply elastic). Diagrams like these are available for many metals and ceramics, and are a useful summary of creep behaviour, helpful in selecting a material for high-temperature applications. 

The various densification mechanisms at different temperatures can be modelled and displayed in HIP diagrams, in which relative temperature is plotted against temperature normalised with respect to the melting-point (Arzt el al. 1983). This procedure relates closely to the deformation-mechanism maps discussed in Section 5.1.2.2. 

Fig. 10.37 Schematic diagram describing the deformation mechanism which results in improved adhesion of hard/soft coatings produced by the MAiC process (courtesy Aveka, Woodbury, MN, USA).

So-called deformation mechanism maps allow to read off the dominant mechanism under different conditions. Figure 11.9 shows a schematic deformation mechanism map. In the diagram, the temperature and the external... 

Diagrams like this can be compiled for different materials and material states. Figure 11.10 shows the deformation mechanism maps of aluminium and tungsten at a grain size of 32 pm. Although both maps have the same overall structure as the schematic map from figure 11.9, they nevertheless differ in the size and exact shape of the different regions. 

The authors of papers [6, 7] found out, that the introduction of particulate nanofiller (calciiun carbonate (CaCOj)) into high density polyethylene (HDPE) results in nanocomposites HDPE/CaCOj impact toughness in comparison with the initial polymer by about 20%. The authors [6, 7] performed this effect detailed fractographic analysis and explained the observed increase by nanocomposites HDPE/CaCOj plastic deformation mechanism change in comparison with the initial HDPE. Without going into details of the indicated analysis, one should note some reasons for doubts in its correctness. In Figure 9.1 the schematic diagrams load-time... 

Creep data of this nature are represented pictorially for some well-studied systems in the form of stress-temperature diagrams, which are termed deformation mechanism maps. These maps indicate stress-temperature regimes (or areas) over which various mechanisms operate. Constant-strain-rate contours are often also included. Thus, for some creep situation, given the appropriate deformation mechanism map and any two of the three parameters—temperature, stress level, and creep strain rate—the third parameter may be determined. 

As an example, for room-temperature applications most metals can be considered to be truly elastic. When stresses beyond the yield point are permitted in the design, permanent deformation is considered to be a function only of applied load and can be determined directly from the stress-strain diagram. The behavior of most plastics is much more dependent on the time of application of the load, the past history of loading, the current and past temperature cycles, and the environmental conditions. Ignorance of these conditions has resulted in the appearance on the market of plastic products that were improperly designed. Fortunately, product performance has been greatly improved as the amount of technical information on the mechanical properties of plastics has increased in the past half century. More importantly, designers have become more familiar with the behavior of plastics rather than... 

Creep modeling A stress-strain diagram is a significant source of data for a material. In metals, for example, most of the needed data for mechanical property considerations are obtained from a stress-strain diagram. In plastic, however, the viscoelasticity causes an initial deformation at a specific load and temperature and is followed by a continuous increase in strain under identical test conditions until the product is either dimensionally out of tolerance or fails in rupture as a result of excessive deformation. This type of an occurrence can be explained with the aid of the Maxwell model shown in Fig. 2-24. 

In terms of the mechanical behavior that has already been described in Sections 5.1 and Section 5.2, stress-strain diagrams for polymers can exhibit many of the same characteristics as brittle materials (Figure 5.58, curve A) and ductile materials (Figure 5.58, curve B). In general, highly crystalline polymers (curve A) behave in a brittle manner, whereas amorphous polymers can exhibit plastic deformation, as in... 

The diagram shows the relationship of the three forms of an SMA as a function of the temperature and pressure to which the material is exposed. Notice that it is possible to convert twinned martensite to deformed martensite without any change in temperature, but only by increasing the pressure on the material. When deformed martensite is produced by this mechanism, it has only one crystallographic structure, a monoclinic form. Deformed martensite can also be produced directly from austenite by the application of sufficient stress on the latter material. 

Figure 6.2. Schematic diagram of probable mechanism of plastic fatigue wear (from Briscoe and Evans, 1987) (a) Formation of plastically deformable grooves in series (b) Deformation of the grooves pushed in one direction (c) Sway back to the opposite direction (d) Deterioration of ridges after repeated fluttering (e) Detachment of ridges in the form of band-shaped debris.

A survey of the load-deformation curves for linear polymers at different temperatures is given in Fig. 25.1A. Each mechanism is further illustrated by a schematic diagram (Figs. 25.1B-E). The mathematical equations for the different mechanisms were given in the Chaps. 13-15. Based on the respective equations Ahmad and Ashby designed Failure Mechanism Maps. The most important of these are reproduced here as Fig. 25.2A-D. 

The deformation of the lattice as a result of the mechanical working is seen from the broadening of the lines in the X-ray diffraction picture, which are narrow under normal circumstances (Debye-Scherrer or powder diagram). 

Fig. 10 shows a typical Heckel diagram. Deviations from linearity often occur at low and high pressures. These are to be expected. At low pressures, reduction in porosity is largely by particle rearrangement, and thus the true consolidation mechanism, i.e., fragmentation or deformation, will be a minor component of the total consolidation process. At high pressures, porosity can become very low and hence its reciprocal becomes a very large number. 

The method developed in this book is also used to provide input parameters for composite models which can be used to predict the thermoelastic and transport properties of multiphase materials. The prediction of the morphologies and properties of such materials is a very active area of research at the frontiers of materials modeling. The prediction of morphology will be discussed in Chapter 19, with emphasis on the rapidly improving advanced methods to predict thermodynamic equilibrium phase diagrams (such as self-consistent mean field theory) and to predict the dynamic pathway by which the morphology evolves (such as mesoscale simulation methods). Chapter 20 will focus on both analytical (closed-form) equations and numerical simulation methods to predict the thermoelastic properties, mechanical properties under large deformation, and transport properties of multiphase polymeric systems. 

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