Permanent Deformation of Materials

The task of this chapter is to introduce the key concepts (both continuum and discrete) used in thinking about dislocations with the aim of explaining a range of observations concerning plastic deformation in crystalline solids. In the opinion of the author, one of the primary conclusions to emerge from the discussions to be made here is that despite the fact that the theory of a single dislocation has reached a high level of sophistication, the promise of dislocation-based models of plasticity with predictive power remains elusive. One reason for this is the fact that true 

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Creep describes time-dependent permanent deformation of materials resulting from constant structural stress. The creep of polymers can be divided into two main stages primary creep and steady-state creep. The creep strain rate decreases with time in the primary creep and is constant in the steady-state creep. Strain recovery occurs with the removal of external load after a creep time. Therefore, the total strain (e) consists of three separate parts el, e2, and e3. The el and e2 are the immediate elastic deformation and delayed elastic deformation, respectively. The e3 is the Newtonian flow. It was found that the el and e2 decreased with increasing clay contenf indicating lower creep recovery with the addition of C20A. The creep compHance J, the ratio of strain and applied load, can be expressed as... 

Yield strength or tensile proof stress the maximum stress that can be applied without permanent deformation of the test specimen. For the materials that have an elastic limit (some materials may not have an elastic region) this may be expressed as the value of the stress on... 

Figure 5.14 shows the microhardnesses for the resins and for their composites. The microhardness perpendicular to the fibres is proportional to the yield stress required to permanently deform the material, while the microhardness parallel to the fibre is more affected by elastic modes of deformation. There is also a great variation in microhardness in the composites depending on the localized resin concentration. The limits of variation are shown in Fig. 5.14 with lower microhardness values indicating a resin-rich area, and higher microhardness values indicating that less resin is present. The limits shown are one standard deviation from the mean. 

To achieve the desired pressure containment at elevated temperatures, most pressure vessels are made of metal or metal alloys. Suitable materials must be ductile that is, the material must expand (strain) with applied pressure (stress). It is important to select a material of construction that is in its proportional range such that the strain is linear, or proportional, to the stress. In this region, the proportionality is called Young s modulus. At sufficiently high stress (the proportional limit), the strain will be more than that predicted by the linear ratio. Up to this point, the material will return to its original dimensions when the stress is removed. Above the proportional limit, permanent deformation will occur and the material will not completely return to its original dimension when the stress is removed. The yield point of many materials is defined as the stress at which a permanent deformation of 0.2% is measured. 

Creep Permanent deformation of a bonded joint or a material after mechanical stress. In bonding technology, important for adhesive layers. 

The point at which permanent deformation of a stressed specimen begins to take place. Stress at which strain increases without accompanying increase in stress. Only materials that exhibit yielding have a yield point. 

Another form of failure for some materials is creep. Creep is a very slow, but permanent deformation of a material imder load. Some plastic materials are subject to creep failures. The cross-sectional area of a part may change and weaken the part as a result of creep. Another example is aluminum electrical wire. During a shortage of copper in the late 1970s, manufacturers substituted solid aluminum for solid copper in some electrical wiring applications. Tight connector screws became loose later as the local load of the connector on the aluminum wire caused creep in the aluminum material. That does not occur for copper wires. In some cases the loose connections for aluminum wires eventually led to arcing and fire. 

The yield strength (YS) of a material, denoted or is the stress corresponding to the end of the linear portion of the stress-strain curve for the uniaxial tensile test. The 0.002 (or 0.001) proof strength (i.e., 0.2% offset yield strength) is used when the material shows no pronounced yield point. Afterward any additional stress leads to a residual permanent deformation of the material i.e., plastic deformation) indicated by a hysteresis. 

Creep Time-dependent permanent deformation of a material under the application of a constant applied stress. 

To overcome friction, the tangential force must be applied over the entire sliding distance the product of the two is friction work. The resulting energy is lost to heat in the form of frictional heating and to other general increases in the entropy of the system, as represented, for example, in the permanent deformation of the surface material. Thus, fiiction is clearly a process of energy dissipation. 

As we note in Section 7.2, the permanent deformation of most crystalline materials is by the motion of dislocations. In addition, the Burgers vector is an element of the theory that has been developed to explain this type of deformation. 

The hardness of a material is usually defined as the resistance to deformation and is usually measured as the permanent deformation of a surface by a specifically shaped indenter under a given load. This does not give an indication of the plastic deformation associated with loading. The hardness of a material may be influenced by grain size, dispersed phases, defect structure, microstructure, density, temperature, deformation rate, etc. For films and coatings there may be substrate influences on the deformation that affect the measurements. As a rule, the coating should be ten times the indentation depth to obtain meaningful results. Surface effects may also influence the measurements for thin films, particularly those with oxide layers. 

Polymers will be elastic at temperatures that are above the glass-transition temperature and below the liquiflcation temperature. Elasticity is generally improved by the light cross linking of chains. This increases the liquiflcation temperature. It also keeps the material from being permanently deformed when stretched, which is due to chains sliding past one another. Computational techniques can be used to predict the glass-transition and liquiflcation temperatures as described below. 

An elastic impression material must be easily and quickly prepared set quickly to an elastic mass in the mouth not be harmful or cause discomfort to the oral tissues and flow to all areas without the need of excessive force. It also must copy detail accurately possess sufficient strength, toughness, and elasticity to resist permanent deformation when removed from the mouth not adversely affect the set properties of the cast material be capable of being... 

Agar-based impression materials must have a compressive strength of at least 0.2 MPa (29 psi). They should have a strain in compression of 4—20% in stresses of 9.8-98 kPa (1.4—14.2 psi) per specification test method, and should not have a permanent deformation exceeding 3% after 12% strain is appHed for 30 seconds. 

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