Design analysis process

The nature of design analysis obviously depends on having product-performance requirements. The product's level of technical sophistication and the consequent level of analysis that can be justified costwise basically control these requirements. The analysis also depends on the design criteria for a particular product. If the design is strength limited, to avoid component failure or damage, or to satisfy safety requirements, it is possible to confine the design analysis simply to a stress analysis. However, if a plastic product is stiffness limited, to avoid excessive deformation from buckling, a full stress-strain analysis will likely be required. Even though many potential factors can influence a design analysis, each application fortunately usually involves only a few factors. For example, TPs' properties are dominated by the viscoelasticity relevant to the applied load. Anisotropy usually dominates the behavior of long-fiber RPs and so on.

The design analysis processes for metals, plastics, and RPs are essentially the same, However due to a certain degree of differences, they sometimes appear to be drastically different. Experience of design analysis can be misleading if applied without consideration to plastics and RPs behaviors. The design analysis process is composed essentially of the three main steps: (a) assessment of stress and strain levels in the proposed design; (b) comparison of critical stress and/or deformation values with design criteria to ensure that the proposed design will satisfy product requirements and materials limitations; and (c) modification of the proposed design to obtain optimum satisfaction of product requirement.

For metallic materials, component design is usually strength limited so that the design criteria in step (b) are often defined in terms of materials strength values, that is, in terms of a maximum permissible stress. Even when the design criterion is avoidance of plasdc flow, rather than avoidance of material failure, the criterion is specified by the limiting yield stress. In these cases, step (a) is only required to provide an analysis of the stress distribudon in the component, and the strain and deformadon distribudons are of little practical interest. These conclusions are a consequence of the relatively high stiffness of metals, and the principal exception is the deformation of thin sections that may lead to buckling.

A further simplification can often arise if the stress analysis problem required in step (a) is statically determinate. In particular, this requires that the externally applied constraints (or boundary conditions) can all be expressed in the form of applied loads and not in terms of imposed relative displacements. The stress distribution depends on the applied loads and on the component geometry, but not on the material stiffness properties. Thus, it is identical for all materials, whether diey be elastic, rigid, or any other form, provided only that the material is sufficiently stiff for satisfaction of the assumption that the applied loads can be considered to be applied to the undeformed, rather than deformed, component geometry.

Thus, for metallic materials in many idealized practical situations, the design process is simplified to a stress (but not strain or displacement) analysis followed by comparison and optimization with critical stress values. When the problem is not statically determinate, the stress analysis requires specification of material stiffness values, but the associated strain and deformation values are usually not required. Since the material behavior is usually represented adequately by linear isotropic elasticity, the stress analysis can be limited to that form, and there are many standard formulae available to aid the designer.

For plastics (unreinforced), the emphasis is somewhat different. Due to their relatively low stiffness, component deformations under load may be much higher than for metals, and the design criteria in step (b) are often defined in terms of maximum acceptable deflections. Thus, for example, a metal panel subjected to a transverse load may be limited by the stresses leading to yield and to a permanent dent. Whereas a plastics panel may be limited by a maximum acceptable transverse deflection even though the panel may recover without permanent damage upon removal of the loads. Even when the design is limited by material failure, it is usual to specify the materials criterion in terms of a critical failure strain rather than a failure stress. Thus, it is evident that strain and deformation play a much more important role for plastics than they do for metals. As a consequence, step (a) is usually required to provide a full stress/strain/deformation analysis and, because of the viscoelastic nature of plastics, this can pose a more difficult problem than for metals.

A particular distinction between the mechanical behaviors of metals and plastics is explained in order to avoid a possible confusion that could have arisen from the preliminary review. A typical stress/strain curve for a metal, exhibits a linear elastic region followed by yield at the yield stress, plastic flow, and ultimately failure at the failure stress. Yield and failure occur at corresponding strains, and one could define yield and failure in terms of these critical strains. This is not common practice because it is simpler in many cases to restrict step (a) to a stress analysis alone. By comparison, it may appear strange that it was stated above that plastics failure criteria are usually defined in terms of a critical strain (rather than stress) and, by comparison with the metals case, switching back from strain to stress may appear to be a minor operation.

Explanation of this apparent fallacy depends on recognition of the fact that stress and strain are not as intimately related for plastics as they are for metals. This is demonstrated by a set of stress/strain curves for a typical plastic where their loading rates increase. This emphasizes that the stress/strain curve for a plastic is not unique, but depends on the loading type, that is, also on time, frequency, or rate. For example, the stress/strain curves obtained at different loading rates and for metals these curves would essentially coincident. However, the behavior of plastics can be very different at low and high rates, and there is no unique relation between stress and strain since this depends on the loading rate too. It is evident that characterization of failure through a unique failure strain cannot be valid in general, but it can be a good approximation in certain classes of situations such as, for example, at high rates or under creep conditions.

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