Stress Analysis for Plastics

The preceding chapters are intended to provide background for the design of plastic parts. In this chapter we will apply the concepts to the actual design process and show how to make a design that will function. Typical plastics parts are shown in Figs. 4-1, 4-2, and 4-3. 

The design constraints on the part are not too severe since the part is not required to fit in a closely defined space and consequently there is a wide latitude in material and size combinations that can be used to perform the necessary function. In a case like this, economic considerations help in selecting a material and configuration that will perform the support function in the most efficient manner. From a structural standpoint there is only one basic requirement for the part that it support the shelf and its contents. There are two possible modes of failure of the part. The load can excede the tensile strength of the support and it will break. The alternative possibility is that with the load on the shelf, the support will stretch until the outer edge of the 

The first step in the design process is to tentatively select a material for the part. In this case, we would like a material which is readily 

A tensile strength vs stress curve which is usually done at one of the standard ASTM test rates in the range of 10 inches per minute. From this curve it is possible to determine the yield strength, the ultimate tensile strength, the elastic modulus, and the elongation to failure at the testing rate. 

Creep curves at various stress levels and usually at room temperature (20°) and one elevated temperature, frequently the temperature which the supplier feels is the maximum material use temperature. 

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In 1885 Kick proposed another law, based on stress analysis of plastic deformation within the elastic limit, which states that the work required for crushing a given mass of material is constant for the same reduction ratio, that is, the ratio of the initial particle size to the final particle size. This leads to the relation... 

A. T. Liu, Linear Elastic and Elasto-Plastic Stress Analysis for Adhesive Lap Joints, T.A.M. Report No. 410, University of Illinois at Urbana-Champaign (July 1976). 

Another rapid loading condition in underwater applications is the application of external hydrostatic stress to plastic structures (also steel, etc.). Internal pressure applications such as those encountered in pipe and tubing or in pressure vessels such as aerosol containers are easily treated using tensile stress and creep properties of the plastic with the appropriate relationships for hoop and membrane stresses. The application of external pressure, especially high static pressure, has a rather unique effect on plastics. The stress analysis for thick walled spherical and tubular structures under external pressure is available. 

The critical titickness of the peel arm is that thickness which equals the radius of the plastic zone at the crack tip, Vy. From Kinloch and Young [8], a stress analysis for plane stress gives Vy = (Ki/d y/27t, where XT/is... 

Elastic Behavior The assumption that displacement strains will produce proportional stress over a sufficiently wide range to justify an elastic-stress analysis often is not valid for nonmetals. In brittle nonmetallic piping, strains initially will produce relatively large elastic stresses. The total displacement strain must be kept small, however, since overstrain results in failure rather than plastic deformation. In plastic and resin nonmetallic piping strains generally will produce stresses of the overstrained (plasfic) type even at relatively low values of total displacement strain. 

Chapter 4 describes in general terms the processing methods which can be used for plastics. All the recent developments in this area have been included and wherever possible the quantitative aspects are stressed. In most cases a simple Newtonian model of each of the processes is developed so that the approach taken to the analysis of plastics processing is not concealed by mathematical complexity. 

This book is intended primarily for students in the various fields of engineering but it is felt that students in other disciplines will welcome and benefit from the engineering approach. Since the book has been written as a general introduction to the quantitative aspects of the properties and processing of plastics, the depth of coverage is not as great as may be found in other texts on the physics, chemistry and stress analysis of viscoelastic materials, this has been done deliberately because it is felt that once the material described here has been studied and understood the reader will be in a better position to decide if he requires the more detailed viscoelastic analysis provided by the advanced texts. 

Linear viscoelasticity Linear viscoelastic theory and its application to static stress analysis is now developed. According to this theory, material is linearly viscoelastic if, when it is stressed below some limiting stress (about half the short-time yield stress), small strains are at any time almost linearly proportional to the imposed stresses. Portions of the creep data typify such behavior and furnish the basis for fairly accurate predictions concerning the deformation of plastics when subjected to loads over long periods of time. It should be noted that linear behavior, as defined, does not always persist throughout the time span over which the data are acquired i.e., the theory is not valid in nonlinear regions and other prediction methods must be used in such cases. 

Creep and stress relation Creep and stress relaxation behavior for plastics are closely related to each other and one can be predicted from knowledge of the other. Therefore, such deformations in plastics can be predicted by the use of standard elastic stress analysis formulas where the elastic constants E and y can be replaced by their viscoelastic equivalents given in Eqs. 2-19 and 2-20. 

In computing ordinary short-term characteristics of plastics, the standard stress analysis formulas may be used. For predicting creep and stress-rupture behavior, the method will vary according to circumstances. In viscoelastic materials, relaxation data can be used in Eqs. 2-16 to 2-20 to predict creep deformations. In other cases the rate theory may be used. 

This photoelastic stress analysis is a technique for the nondestructive determination of stress and strain components at any point in a stressed product by viewing a transparent plastic product. If not transparent, a plastic coating is used such as certain epoxy, polycarbonate, or acrylic plastics. This test method measures residual strains using an automated electro-optical system. 

Contents Introduction to Materials. Manufacturing Considerations for Injection Molded Parts. The Design Process and Material Selection. Structural Design Considerations. Prototyping and Experimental Stress Analysis. Assembly of Injection Molded Plastic Parts. Conversion Constants. 

S. Okikawa, M. Sakimoto, M. Tanaka, T. Sato, T. Toya, and Y. Kara, Stress Analysis of Passivation Film Crack for Plastic Molded LSI Caused by Thermal Stress, Proc. Internet ional Society for Testing and Failure Analysis, Oct. 1983, Los Angeles, CA. 

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. 

The same stress-optical characteristic also permits examination of locked-in stresses in a molded plastic part. The part is examined under polarized light, and the amount of stress is indicated by the number of fringes or rings that become visible. Illumination with white light gives colorful patterns involving all the colors of the spectrum. Monochromatic light is, however, used for stress analysis because it permits more precise measurements. 

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