Yield and Hardening

The simplest window on the processes that operate when a crystal is subject to plastic deformation is the stress-strain curve. As shown in flg. 2.10, once the stress exceeds the elastic limit, not only is there a marked deviation from linearity, but the crystal is also permanently deformed. If such stresses are reached and the crystal is subsequently unloaded, there will be a residual plastic strain. One conventional measure of the yield point is to consider that stress for which there is a 0.2% residual plastic strain upon unloading. If the sample is reloaded, it will be found that the yield point has moved to higher stresses - the crystal has hardened. 

One of the unifying themes in this book has been the notion of material parameters. We have repeatedly interested ourselves in the existence of quantities that serve to characterize a material under partieular temperatures, loading conditions, and past history. The discussion of the stress-strain curve suggests further candidates. The most immediate suggestion in the present context is that of the yield stress. Despite the presence of some arbitrariness in the definition of the yield stress, if we adopt the convention of the 0.2% offset point, a case can be made for the idea that different materials have reproducible yield stresses. A schematic rendering of the typical scales for the yield stress is given in fig. 8.1 in which it is seen that, for the vast majority of materials, the yield stress is a small fraction of the elastic moduli. 

Tl alloys Low alloy steels Stainless steel Carbon steels Al alloys 

Cu alloys Mild steel Lead alloys (Worked) 

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Unfortunately, this type of model has the drawback that re-yielding and hardening stagnation after re-yielding cannot be fitted to modem steels like dual phase or complex phase steels, which gives the motivation for the short introduction of the following second model. 

An element will have hoth geometric and material properties. Spatially, an element is defined by its nodes however, additional geometric input is usually required for line and surface elements. For structural analysis the minimum material property is the modulus of elasticity. In most cases, Poisson s ratio or shear modulus must also be specified. If an orthotropic material is used then the orientation of the material must be specified as well as the elastic constants relative to each principal axis. If post-yield behavior is to be modelled then an elasto-plastic material model must be applied and the yield and hardening behavior defined. Constitutive adhesive and sealant models are discussed in more detail in O Chap. 23. Additional material properties will also be required for dynamic or thermal analysis. 

Consistency, working time, setting time and hardening of an AB cement can be assessed only imperfectly in the laboratory. These properties are important to the clinician but are very difficult to define in terms of laboratory tests. The consistency or workability of a cement paste relates to internal forces of cohesion, represented by the yield stress, rather than to viscosity, since cements behave as plastic bodies and not as Newtonian liquids. The optimum stiffness or consistency required of a cement paste depends upon its application. 

Air content of freshly mixed concrete by the pressure method Air content of freshly mixed concrete by the volumetric method Unit weight, yield, and air content of concrete Specific gravity, absorption, and voids in hardened concrete Resistance of concrete to rapid freezing and thawing Scaling resistance of concrete surfaces exposed to deicing chemicals... 

The yield point and hardening slope of the interlayer should be low compared to those of the matrix material. 

Fructan was harvested by precipitation from the culture broth by addition of ethanol or isopropanol. Acetone and methanol can also be used. The yield and consistency of the product varied depending on the amount of alcohol added. The fructan started to precipitate at the medium/alcohol v/v ratio of 1 1.2, and the yield peaked at about 1 1.5. Further increase in the ratio hardened the fructan and made the product less fluid. Slightly less isopropanol was needed than ethanol to precipitate levan (fructan). Although most of the bacterial cells, unfermented sugars, and other solubles remained in the aqueous alcohol phase, pre-removal of microbial cells by centrifuging was needed to obtain a pure form of fructan. The product was further purified by repeated precipitation and dissolution in water, followed by dialysis or ultrafiltration. The final product was an... 

At elevated temperatures, the thermal recovery processes described in Section 5.1.2.3 can occur concurrently with deformation, and both strength and strain hardening are consequently reduced. The latter effect results in decreasing the difference between yield and tensile strengths until at sufficiently high temperatures, they are essentially equal. At lower temperatures, temperature has a marked influence on deformation in crystalline materials. Temperature can affect the number of active slip systems in some... 

Even before the discovery of vulcanisation by Goodyear [1], the effects on rubber of heat, light, acids and alkalies were studied. Testing became necessary when early investigators faced problems with rubber and its vulcanisates. Possibly the earliest chemical resistance test on rubber was undertaken by Goodyear when he treated rubber with nitric acid and this yielded a hardened mass [2, 3]. He mistakenly called this phenomenon vulcanisation, before he accidentally discovered vulcanisation with sulfur at a later point. 

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