Applying Stress-Strain Data

The information presented is used in different load bearing equations such as those 

Designers of most structures specify material stresses and strains well within the pro-portional/elastic limit. Where required (with no or limited experience on a particular type product materialwise and/or process-wise) this practice builds in a margin of safety to accommodate the effects of improper material processing conditions and/or unforeseen loads and environmental factors. This practice also allows the designer to use design equations based on the assumptions of small deformation and purely elastic material behavior. Other properties derived from stress-strain data that are used include modulus of elasticity and tensile strength. 

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Shear stress-strain data can be generated by twisting (applying torque) a material specimen at a specified rate while measuring the angle of twist between the ends of the specimen and the torque load exerted by the specimen on the testing machine. Maximum shear stress at the surface of the specimen can be computed from the measured torque that is the maximum shear strain from the measured angle of twist. 

Weakly crosslinked epoxy-amine networks above their Tg exhibit rubbery behaviour like vulcanized rubbers and the theory of rubber elasticity can be applied to their mechanical behaviour. The equilibrium stress-strain data can be correlated with the concentration of elastically active network chains (EANC) and other statistical characteristics of the gel. This correlation is important not only for verification of the theory but also for application of crosslinked epoxies above their Tg. 

Dynamic mechanical measurements are performed at very small strains in order to ensure that linear viscoelasticity relations can be applied to the data. Stress-strain data involve large strain behavior and are accumulated in the nonlinear region. In other words, the tensile test itself alters the structure of the test specimen, which usually cannot be cycled back to its initial state. (Similarly, dynamic deformations at large strains test the fatigue resistance of the material.)... 

This is a useful result, as it means that stress-strain data for load-unload cycles may be used to separate out bond-stretching and conformational contributions to the stress [61]. Thus we may evaluate them as follows, applying equation (4.16) to loading and unloading, and making use of equation (4.17), for any value of elongation where the above restrictions apply (particularly where stress transients can... 

The short-term stress/strain data of different grades of PP (and for other plastics) is of limited use and should only be used for pre-selection of material. In reality, plastic components are seldom designed and subjected to such high levels of strain as applied in short-term tensile tests. In addition, most of the cases of product failure are brittle in nature. Consequently, the long-term creep and fatigue properties of PP, discussed in Sections 4.3.3 to 4.3.5, are more important for structural applications. 

Compressive stress-strain data are required mainly for the modeling of refractory linings, whereas flexural stress-strain measurements are more often applied to individual refractory components such as sliding gate plates or kiln furniture. 

In the perfectly elastic, perfectly plastic models, the high pressure compressibility can be approximated from static high pressure experiments or from high-order elastic constant measurements. Based on an estimate of strength, the stress-volume relation under uniaxial strain conditions appropriate for shock compression can be constructed. Inversely, and more typically, strength corrections can be applied to shock data to remove the shear strength component. The stress-volume relation is composed of the isotropic (hydrostatic) stress to which a component of shear stress appropriate to the... 

Figure 2. Thermal strain vs temperature curves for VsSi measured along [001] on heating (4.2-60K) and cooling (4.2-1.5K). Curve (a) is for an uniaxial stress (s 0.03o doo)) along [001] (b) and (c) are for biaxial stress applied along [100] and [010] with 0.5o (ioo> and o (ioo>, respectively. The x-ray data of Batterman and Barrett (reference 15) are also plotted for comparison. The insets show the directions of applied stresses and [in case of the curve (a)] the martensite-phase domains. (From reference 5)...

Viscoelastic creep data are usually presented in one of two ways. In the first, the total strain experienced by the material under the applied stress is plotted as a function of time. Families of such curves may be presented at each temperature of interest, each curve representing the creep behavior of the material at a different level of applied stress. Below a critical stress, viscoelastic materials may exhibit linear viscoelasticity that is, the total strain at a given time is proportional to the applied stress. Above this critical stress, the creep rate becomes disproportionately faster. In the second, the apparent creep modulus is plotted as a function of time. 

Different viscoelastic materials may have considerably different creep behavior at the same temperature. A given viscoelastic material may have considerably different creep behavior at different temperatures. Viscoelastic creep data are necessary and extremely important in designing products that must bear long-term loads. It is inappropriate to use an instantaneous (short load) modulus of elasticity to design such structures because they do not reflect the effects of creep. Viscoelastic creep modulus, on the other hand, allows one to estimate the total material strain that will result from a given applied stress acting for a given time at the anticipated use temperature of the structure. 

Product performance data Products subjected to a given load develop a corresponding predictable deformation. If it continues to increase without any increase in load or stress, the material is said to be experiencing creep or cold flow. Creep in any product is defined as increasing strain over time in the presence of a constant stress (Figs. 2-25 and 26). The rate of creep for any given plastic, steel, wood, etc. material depends on the basic applied stress, time, and temperature. 

The observed deviations from Gaussian stress-strain behaviour in compression were in the same sense as those predicted by the Mooney-Rivlin equation, with modulus increasing as deformation ratio(A) decreases. The Mooney-Rivlin equation is usually applied to tensile data but can also be applied compression data(33). According to the Mooney-Rivlin equation... 

Stress-strain relationships for soil are difficult to model due to their complexity. In normal practice, response of soil consists of analyzing compression and shear stresses produced by the structure, applied as static loads. Change in soil strength with deformation is usually disregarded. Clay soils will exhibit some elastic response and are capable of absorbing blast-energy however, there may be insufficient test data to define this response quantitatively. Soil has a very low tensile capacity thus the stress-strain relationship is radically different in the tension region than in compression. 

Firstly, it helps to provide a cross-check on whether the response of the material is linear or can be treated as such. Sometimes a material is so fragile that it is not possible to apply a low enough strain or stress to obtain a linear response. However, it is also possible to find non-linear responses with a stress/strain relationship that will allow satisfactory application of some of the basic features of linear viscoelasticity. Comparison between the transformed data and the experiment will indicate the validity of the application of linear models. 

A simple bubble machine is devised and successfully applied in characterising lightly crosslinked PE resins for foam expansion. The biaxial stress-strain relationship is deduced from the air injection rate and pressure. The effects of strain rate, temperatnre and crosslinker level on the stress-strain behavionr are investigated. Uniaxial extension experiments are also performed and compared with biaxial extension data. 5 refs. 

Data can be obtained from tests in uniaxial tension, uniaxial compression, equibiaxial tension, pure shear and simple shear. Relevant test methods are described in subsequent sections. In principle, the coefficients for a model can be obtained from a single test, for example uniaxial tension. However, the coefficients are not fully independent and more than one set of values can be found to describe the tension stress strain curve. A difficulty will arise if these coefficients are applied to another mode of deformation, for example shear or compression, because the different sets of values may not be equivalent in these cases. To obtain more robust coefficients it is necessary to carry out tests using more than one geometry and to combine the data to optimize the coefficients. 

Compressive measurements provide a means to determine specimen stiffness, Young s modulus of elasticity, strength at failure, stress at yield, and strain at yield. These measurements can be performed on samples such as soy milk gels (Kampf and Nussi-novitch, 1997) and apples (Lurie and Nussi-novitch, 1996). In the case of convex bodies, where Poisson s ratio is known, the Hertz model should be applied to the data in order to determine Young s modulus of elasticity (Mohsenin, 1970). It should also be noted that for biological materials, Young s modulus or the apparent elastic modulus is dependent on the rate at which a specimen is deformed. 

Missing from the literature are standardized and comparative physical strength data for adhesives in neat form or as applied to the skin. The most comprehensive examples of the stress-strain relationships of excised human skin are appended (Appendix 2.6.1.) three axes of any material are demonstrated below, where X- and T-axes are lateral (perpendicular to each other), but in the same plane, whereas the Z direction is not in the same plane, but perpendicular to X- and T-axes as demonstrated in Fig. 3.10. 

The criteria for sutureless adhesives are still being developed. Although the criteria are not well defined, the following Table 3.2 embodies certain essential properties that will continue to apply until in vivo testing is complete. These criteria are offered as a template for collecting data after application of adhesives in animals, and the data listed in Table 3.3 are indications of the stress-strain relationships to be expected in humans. 

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