Surface Stresses and Deformations

It can be said that the design of a product involves analytical, empirical, and/or experimental techniques to predict and thus control mechanical stresses. Strength is the ability of a material to bear both static (sustained) and dynamic (time-varying) loads without significant permanent deformation. Many non-ferrous materials suffer permanent deformation under sustained loads (creep). Ductilc materials withstand dynamic loads better than brittle materials that may fracture under sudden load application. As reviewed, materials such as plastics often exhibit significant changes in material properties over the temperature range encountered by a product.

There are examples where control of deflection or deformation during service may be required. Such structural elements are designed for stiffness to control deflection but must be checked to assure that strength criteria are reached. A product can be viewed as a collection of individual elements interconnected to achicve an overall systems function. Each element may be individually modeled; however, the model becomes complex when the elements are interconnected.

The static or dynamic response of one element becomes the input or forcing function for elements adjacent or mounted to it. An example is the concept of mechanical impedance that applies to dynamic environments and refers to the reaction between a structural element or component and its mounting points over a range of excitation frequencies. The reaction force at the structural interface or mounting point is a function of the resonance response of an element and may have an amplifying or damping effect on the mounting structure, depending on the spectrum of the excitation. Mechanical impedance design involves control of element resonance and structure resonance, providing compatible impedance for interconnected structural and component elements.

As an example view a 3-D product that has a balanced system of forces acting on it, Fj through F5 in Fig. 3.7, such that the product is at rest. A product subjected to external forces develops internal forces to transfer and distribute the external load. Imagine that the product in

FORCE VECTORS

Fig. 3.7 is cut at an arbitrary cross-section and one part removed. To keep the body at rest there must be a system of forces acting on the cut surface to balance the external forces. These same systems of forces exist within the uncut body and are called stresses. Stresses must be described with both a magnitude and a direction. Consider an arbitrary point, P, on the cut surface in the figure where the stress, S, is as indicated. For analysis, it is more convenient to resolve the stress, S, into two stress components. One acts perpendicular to the surface and is called a normal or direct stress, a. The second stress acts parallel to the surface and is called a shear stress, X.

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