Metals, stress, strain

Considerable attention is given in the Institute to the application of the methods of acoustic emission and optical holography for engineering diagnostics of the service life and the stressed-strained state of welded metal structures. 

Table 10-56 gives values for the modulus of elasticity for nonmetals however, no specific stress-limiting criteria or methods of stress analysis are presented. Stress-strain behavior of most nonmetals differs considerably from that of metals and is less well-defined for mathematic analysis. The piping system should be designed and laid out so that flexural stresses resulting from displacement due to expansion, contraction, and other movement are minimized. This concept requires special attention to supports, terminals, and other restraints. 

Shock loading in most metals and alloys produces greater hardening than quasi-static deformation to the same total strain, particularly if the metal undergoes a polymorphic phase transition, such as is observed in pure iron [1]-[10]. Figure 6.1 compares the stress-strain response of an annealed... 

When metals are rolled or forged, or drawn to wire, or when polymers are injection-moulded or pressed or drawn, energy is absorbed. The work done on a material to change its shape permanently is called the plastic work- its value, per unit volume, is the area of the cross-hatched region shown in Fig. 8.9 it may easily be found (if the stress-strain curve is known) for any amount of permanent plastic deformation, e. Plastic work is important in metal- and polymer-forming operations because it determines the forces that the rolls, or press, or moulding machine must exert on the material. 

The result is work-hardening the steeply rising stress-strain curve after yield, shown in Chapter 8. All metals and ceramics work-harden. It can be a nuisance if you want to roll thin sheet, work-hardening quickly raises the yield strength so much that you have to stop and anneal the metal (heat it up to remove the accumulated dislocations) before you can go on. But it is also useful it is a potent strengthening method, which can be added to the other methods to produce strong materials. 

In many respects the stress-strain graph for a plastic is similar to that for a metal (see Fig. 1.2). 

Shear-stress-shear-strain curves typical of fiber-reinforced epoxy resins are quite nonlinear, but all other stress-strain curves are essentially linear. Hahn and Tsai [6-48] analyzed lamina behavior with this nonlinear deformation behavior. Hahn [6-49] extended the analysis to laminate behavior. Inelastic effects in micromechanics analyses were examined by Adams [6-50]. Jones and Morgan [6-51] developed an approach to treat nonlinearities in all stress-strain curves for a lamina of a metal-matrix or carbon-carbon composite material. Morgan and Jones extended the lamina analysis to laminate deformation analysis [6-52] and then to buckling of laminated plates [6-53]. 

Let s address the issue of nonlinear material behavior, i.e., nonlinear stress-strain behavior. Where does this nonlinear material behavior come from Generally, any of the matrix-dominated properties will exhibit some degree of material nonlinearity because a matrix material is generally a plastic material, such as a resin or even a metal in a metal-matrix composite. For example, in a boron-aluminum composite material, recognize that the aluminum matrix is a metal with an inherently nonlinear stress-strain curve. Thus, the matrix-dominated properties, 3 and Gj2i generally have some level of nonlinear stress-strain curve. 

Spannungs-freiglUhen, n. Metal.) stress-relief anneal, -grad, m. degree of tension, spannungslos, a. without tension or strain Elec.) dead. 

Hydrogen effect on the mechanical properties discussed below was studied on several a and a+fi alloys with the following nominal composition of metallic components (Russian trade marks given in parentheses) commercial titanium of nominal purity 99.3% (VTl-0), Ti-6Al-2Zr-1.5V-lMo (VT20), Ti-6A1-4.5V (VT6), Ti-6Al-2.5Mo-2Cr (VT3-1), Ti-4Al-1.5Mn (OT4), Ti-6.5Al-4Mo-2Sn-0.6W-0.2Si (VT25u) and others. The main features of their stress-strain behavior due to hydrogenation were much similar, but some individuality was characteristic of each alloy. 

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 conclusion regarding creep testing, it can be stated that creep data and a stress-strain diagram indicate whether plain plastic properties can lead to practical product dimensions or whether a RP has to be substituted to keep the design within the desired proportions. For long-term product use under continuous load, plastic materials have to consider creep with much greater care than would be the case with metals. 

However, not all properties are improved by filler. One notable feature of the mechanical behaviour of filled elastomers is the phenomenon of stresssoftening. This manifests itself as a loss of stiffness when the composite material is stretched and then unloaded. In a regime of repeated loading and unloading, it is found that part of the second stress-strain curve falls below the original curve (see Figure 7.13). This is the direct opposite of what happens to metals, and the underlying reasons for it are not yet fully understood. 

Most engineering materials, particularly metals, follow Hooke s law by which it is meant that they exhibit a linear relationship between elastic stress and strain. This linear relationship can be expressed as o = E where E is known as the modulus of elasticity. The value of E, which is given by the slope of the stress-strain plot, is a characteristic of the material being considered and changes from material to material. 

It has been found that in the case of many metals the observed stress-strain data approximately follow the empirical relationship o = k1 s " (n < 1), where kj and n are constants that vary from material to material. Taking logarithms one can write... 

The modulus of elasticity of a material it is the ratio of the stress to the strain produced by the stress in the material. Hooke s law is obeyed by metals but mbber obeys Hooke s law only at small strains in shear. At low strains up to about 15% the stress-strain curve is almost linear, but above 15% the stress and strain are no longer proportional. See Modulus. 

Figure 2.5 Schematic stress-strain curve for a metallic specimen such as wrought iron or mild steel...

Likewise, the mechanical properties of the copolymers were nearly identical or even somewhat enhanced towards the polyimide homopolymer in terms of the modulus and tensile strength values [44,47]. For most of the block copolymers, the elongations to break were substantially higher than that of PMDA/ODA polyimide (Table 4). The shape of the polyimide stress-strain curve is similar to that of a work-hardened metal with no distinguishable yield point... 

A number of physical tests emphasizing stress-strain behavior will be covered in Chapter 14. Here, we will concentrate on other areas of testing, emphasizing thermal and electrical properties and on the characterization of polymers by spectral means. Spectroscopic characterization generally concentrates on the structural identification of materials. Most of these techniques, and those given in Chapter 14, can also be directly applied to nonpolymeric materials such as small organic molecules, inorganic compounds, and metals. 

Figure 5.77 Comparison of idealized stress-strain diagrams for metals, amorphous polymers, and elastomers.

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