Hoop stretching

For preform design purposes, three relationships are used the axial or longitudinal stretch ratio (SRj), the circumferential or hoop stretch ratio (SR ), and the BUR, which are defined as follows ... 

Note that the ratio of the ratio of the hoop stress (pR/h) to the axial stress (pR/lh) is only 2. From the data in this question the hoop stress will be 8.12 MN/m. A plastic cylinder or pipe is an interesting situation in that it is an example of creep under biaxial stresses. The material is being stretched in the hoop direction by a stress of 8.12 MN/m but the strain in this direction is restricted by the perpendicular axial stress of 0.5(8.12) MN/m. Reference to any solid mechanics text will show that this situation is normally dealt with by calculating an equivalent stress, Og. For a cylinder under pressure Og is given by 0.5hoop stress. This would permit the above question to be solved using the method outlined earlier. 

Blanck H, Admrraal W, eleven REMJ, Guasch H, van den Hoop MAGT, Ivorra N, Nystrom B, Paulsson M, Petterson RP, Sabater S, Tubbing GMJ (2003) Variability in zinc tolerance, measured as incorporation of radio-labeled carbon dioxide and thymidine, in periphyton communities sampled from 15 European river stretches. Arch Environ Contam Toxicol 44 17... 

Stretch thinly woven fabric over an embroidery hoop and dip the hoop into the tray, spreading the mixture evenly over the cloth. 

Almost 75% of processed plastics are EBM, almost 25% are IBM, and about 1% use other techniques. About 75% of all IBM products are stretched biaxially there are also stretched EBM. With stretched blow molding orientation takes place simultaneously in the hoop and longitudinal directions. These BM processes offer different advantages in producing different types of products based on the plastics to be used, performance requirements, production quantity, and costs. The parts are formed in a mold that defines the external shape only. As the... 

Stretch-blow processing is used to develop biaxial molecular orientation. If blow pressure alone were used, the stresses in the preform wall would be predominantly circumferential, producing orientation only in the hoop direction of the bottle. However, the additional stresses generated longitudinally by the stretch rod result in biaxial orientation. 

The melt bubble is stretched vertically and circumferentially by a factor of 2 or more, so that an initial melt thickness of about 1 mm is reduced to between 250 and 100 pm. In the biaxial tensile flow, the melt stress in the hoop (H) direction can be calculated from the pressure p inside the bubble, the current bubble radius r and thickness t, using Eq. (C.22) of Section C.3. 

When a thin membrane is stretched over a cylindrical hoop, the drumhead surface movement w r,t) obeys the approximate force balance... 

In stretch blow molding, there are two ratios that multiply together to provide the blow up ratio BUR. In extrusion blow molding, there is only the hoop ratio (that is the blow-up ratio). In stretch blow molding there is the hoop that is multiplied by the axial ratio. Thus, BUR = Hoop ratio x axial ratio. 

To check if the orientation is correct, a dog bone can be cut from the stretch blow-molded PET container and a tensile test conducted on an Instron or similar machine. A dog bone shape is cut in the hoop direction and one is cut in the axial direction. PET has a base strength of approximately 46 MPa (6700 psi). If the hoop ratio is 5, then in the container in the hoop direction, the tensile strength should be approximately 231 MPa (33,500 psi). If the axial ratio is 2, then the tensile strength in the vertical direction would approximately be 92 MPa (13,400 psi). 

Orientation processes also take place in blow-molding operations. A particularly significant aspect is biaxial stretch blow molding, in which the polymer preform is stretched both in the hoop and axial directions. 

Two ratios involving preform-to-product dimensions are utilized to describe biaxial stretch molding. The first of these is the hoop ratio H ... 

Fabric samples can be stretched across a frame (a small embroidery hoop is excellent for this application) to give a flat, nonwrinkled surface. Backing the sample with light trap ensures that external light does not affect measurements. Yarn or pile samples can be bunched, bound, and then cut flat across the pile to give a flat surface to present to the sphere port. 

PLA bottles are formed by injection stretch blow molding (ISBM). This process induces biaxial orientation of PLA bottle in the axial and hoop directions, which results in much improved mechanical and barrier properties compared to injection molded PLA. The molecular orientation induced during the ISBM process decreases the effect of aging by stabilizing the polymer free volume [21]. The crystallites... 

One of the major advantages of stretch blow molding is the ability to stretch the preform in both the hoop direction and the axial direction. This biaxial stretching of material increases the tensile strength, barrier properties, drop impact, clarity, and top load in the container. With these increases it is usually possible to reduce the overall weight in a container by 10 to 15 percent less than when producing a container in another way. 

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