Case studies 219

10.4 Case studies 219

there is a more serious dimension. Producers of foods, drugs, chemicals, even washing powder, now package their products in ‘break to access’ packaging so that the purchaser knows that it has not been tampered with. How do you arrange protection and yet enable fracture? One part of the answer is to choose the right material; the other is to provide stress concentrations to focus stress on the break-lines or to use adhesives that have high shear strength but low peel resistance.

Start with material: materials with low ductility, in thin sheets, tear easily. If ‘opening’ means pulling in such a way as to tear (as it often does), then the first step is a to choose a material with adequate stiffness, strength and durability, but low ductility. The lids of top-opening drinks cans are made of a different alloy than the can itself for exactly this reason.

Next, stress concentration. This means reducing the section by grooving or serrating the package locally along the line where tearing is wanted. Toilet paper, as we all know, hardly ever tears along the perforations, but it was the right idea. The sardine can on the cover of this chapter is made of low-ductility aluminum alloy with a groove with a sharp radius of curvature along the tear line to provide a stress concentration factor (Chapter 7) of

where c is the groove depth and ρ its root radius and the factor 1 ⁄ 2 appears because the loading is shear rather than tension. A 0.2 mm groove with root radius of 0.02 mm gives a local stress that is 2.5 times higher than that else- where, localizing the tearing at the groove.

The peel-strip of a CD wrapper is not a groove; it is an additional thicker strip. How does this apparent reinforcement make it easier to tear open the package? Figure 7.7 provides the answer: it is because any sudden change of sec- tion concentrates stress. If the strip thickness is c and the radius where it joins the wrapping is ρ, the stress concentration is still given by equation (10.22).

The alternative to tearing is adhesive peeling. Figure 10.11 shows an adhe- sive joint before and during peeling. The adhesive has shear strength σ s * and toughness G c *. Adhesively bonded packaging must accept in-plane tension, since to protect the content it must support the mass of its contents and hand- ling loads. The in-plane pull force F t that the joint can carry without failing is

F t ⫽σ *A⫽σ s *wL s

where A ⫽ wL is the area of the bonded surface. To open it, a peel force F p is applied. The lower part of Figure 10.11 shows how F p does work when the joint is peeled back by a distance δx, creating new surface of area w δx. This requires

and energy G c * w δx (since G c *, the toughness, is the energy to create unit area of new surface). The work done by F p must provide this energy, giving

220 Chapter 10 Keeping it all together: fracture-limited design

Figure 10.11 Peeling of an adhesive bond.

F p δx ⫽ G c * w δx

Thus, F p ⫽wG c * The ratio of the peel force to the tensile force is

Adhesive joints are designed to have a particular value for this ratio. The choice of adhesive sets the values of G * and σ c *, allowing the length L to be chosen to s give tensile strength with ease of peeling.