Isotropic / -plasticity

Resin. A natural or synthetic substance, usually organic in composition, characterized by being amorphous, isotropic, plastic, often sticky, and usually fusible and soluble at some stage in its manufacture or processing. 

The critical values are generally obtained from a standard tensile test. Once the critical values are obtained the application of any (or all) of these criteria in conjunction with a dependable stress analysis is straightforward. Here we demonstrate the method by a simple example. Let us assume that it is desired to determine the torque required to cause failure of a 25 mm in diameter shaft constructed of an homogeneous isotropic plastic with a failure stress in tension, o, of 7 x 10 N/m. Assume further tlmt the modulus of elasticity, E, for this plastic is given by 3 x 10° N/m, and that is has a Poisson ratio of 0.3. We will explore the prediction of the three criteria just discussed. 

Isocyanate bonding agent, 85 Isonox 129, 546-548 Isotactic, 57, 59, 67 Isothermal operation, 575 Isotropic plastics, 56 Izod impact resistance, 70... 

Poisson s ratio itself is a complex quantity, as there is a phase lag between the lateral motions and the in-plane stress and strain of a dynamically stressed system. Most isotropic plastics and rubbers have Poisson s ratios of 0.3 and 0.5 approximately respectively, but it... 

Closed-form analytical solution (using an isotropic plastic material model) Fast and easy to perform More accurate than a linear elastic solution Handbook solutions are available only for very few geometries and loading conditions May give inaccurate results... 

FE analysis using a simple material model (e.g., linear elastic, hyperelastic, linear viscoelastic, isotropic plasticity) Can account for complex geometries Relatively easy to perform Does not consider the true material behavior in general deformation states Typically valid only for small-intermediate deformations May give inaccurate results... 

What are the main disadvantages of isotropic plasticity as a material model for UHMWPE ... 

Second, the growth process allows a variety of routes to the formation of fibers but there are no simple way s to form a dense isotropic plastic. Thus, even essentially isotropic materials will have a fibrous composite microstmcture. Weiner et al. (2000) have argued that many biological structures can be viewed as a search for isotropic properties, or at least orthotropic properties (strong in two dimensions), from fibrous materials. This would reflect the unpredictability of stresses encountered by a structure in a dynamic environment. 

Closed-form analytical solution (e.g., using an isotropic plastic material model) [4]... 

Computer-assisted analytical solution for simple geometries (e.g., isotropic plasticity, linear viscoelasticity, hyperelasticity)... 

Dimensional Stability. Plastics, ia general, are subject to dimensional change at elevated temperature. One important change is the expansion of plastics with increa sing temperature, a process that is also reversible. However, the coefficient of thermal expansion (GTE), measured according to ASTM E831, frequendy is not linear with temperature and may vary depending on the direction in which the sample is tested, that is, samples may not be isotropic (Eig. 7). 

In this section, the general inelastic theory of Section 5.2 will be specialized to a simple phenomenological theory of plasticity. The inelastic strain rate tensor e may be identified with the plastic strain rate tensor e . In order to include isotropic and kinematic hardening, the set of internal state variables, denoted collectively by k in the previous theory, is reduced to the set (k, a) where k is a scalar representing isotropic hardening and a is a symmetric second-order tensor representing kinematic hardening. The elastic limit condition in stress space (5.25), now called a yield condition, becomes... 

In the classical theory of plasticity, constitutive equations for the evolution of the isotropic and kinematic hardening parameters are usually expressed as... 

Atluri, S.N., On Constitutive Relations at Finite Strain Hypo-Elasticity and Elasto-Plasticity with Isotropic or Kinematic Hardening, Comput. Methods Appl. Mech. Engrg. 43, 137-171 (1984). 

Wallace [15], [16] gives details on effects of nonlinear material behavior and compression-induced anisotropy in initially isotropic materials for weak shocks, and Johnson et ai. [17] give results for infinitesimal compression of initially anisotropic single crystals, but the forms of the equations are the same as for (7.10)-(7.11). From these results it is easy to see where the micromechanical effects of rate-dependent plastic flow are included in the analysis the micromechanics (through the mesoscale variables and n) is contained in the term y, as given by (7.1). 

The change in shape of a material when it is subjected to a change in temperature is determined by the coefficient of thermal expansion, aj- Normally for isotropic materials the value of aj will be the same in all directions. For convenience this is often taken to be the case in plastics but one always needs... 

Example 3.15 A sandwich moulding is made up of solid skins with a foamed plastic core. The skins and core may be regarded as isotropic with the following the properties ... 

A plastic composite is made up of three layers of isotropic materials as follows ... 

The Z-direction is perpendicular to the page. For simplicity the material is assumed to be isotropic, ie same properties in all directions. However, in some cases for plastics and almost always for fibre composites, the properties will be anisotropic. Thus E and v will have different values in the x, y and z direction. Also, it should also be remembered that only at short times can E and v be assumed to be constants. They will both change with time and so for long-term loading, appropriate values should be used. 

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... 

Fig. 2.8. Idealized elastic/perfectly plastic solid behavior results in a stress tensor in which there is a constant offset between the hydrostatic (isotropic) loading and shock compression. Such behavior is only an approximation which may not be appropriate in many cases.

Perhaps the most dramatic exception to the perfectly elastic, perfectly plastic materials response is encountered in several brittle, refractory materials that show behaviors indicative of an isotropic compression state above their Hugoniot elastic limits. Upon yielding, these materials exhibit a loss of shear strength. Such behavior was first observed from piezoelectric response measurements of quartz by Neilson and Benedick [62N01]. The electrical response observations were later confirmed in mechanical response measurements of Waekerle [62W01] and Fowles [61F01]. 

Let us enter the world of liquid crystals built by the purely entropic forces present in hard body systems. The phase diagram of hard spherocylinders (HSC) shows a rich variety of liquid crystalline phases [71,72]. It includes the isotropic, nematic, smectic A, plastic, and solid phases [73]. In a plastic crystal the particle centers lie on lattice sites, but the orientations of the... 

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