Tensile strength to weight conversion

Question

I read in a documentation to some adhezive: the tensile strength is 13 N/mm². How many kilograms can the 10x10mm bonding hold?

I tried to calculate it by the following:

$$\begin{align} F &= m/g \\ \therefore m &= Fg \end{align}$$

the strength is in N/mm² e.g. that is

$$\begin{align} p = F/A \\ \therefore F = pA \end{align}$$

substituting the $F$ in $m = Fg$, I got

$$m = pAg$$

Using real numbers, - tensile strength = 13 N/mm² = 13*10e6 N/m² - A = 10x10mm (100mm² = 0.0001m²)

$$m = 13*10e6 * 0.0001 * 9.81 = 12753 \text{ kg} $$

The result doesn't look right - the 10x10mm bonding imho can't hold 13.000kg weight.

Where did I make a mistake? So the question is: how to convert the 13 N/mm² tensile strength to kilograms (e.g. how many kilos I can hang to the bonded 10x10mm plates?)

Answer 1

Pay attention to your unit analysis. You multiplied by the acceleration due to gravity, rather than dividing by it. Unit analysis would have shown this to be nonsense.

$$13 \frac{N}{mm^2} \cdot 100 mm^2 = 1300 N = 1300 \frac{kg \cdot m}{s^2}$$

Therefore, to get kg, you need to divide by an acceleration:

$$\frac{1300 \frac{kg \cdot m}{s^2}}{9.81 \frac{m}{s^2}} = 132.5 kg$$

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EDIT: In terms of the symbolic analysis, your very first statement was wrong: Force equals mass times acceleration, so you should have written it as

$$F = m\cdot g \text{ and } m = \frac{F}{g}$$

Then, when you combine that with the equation for pressure, you get

$$m = \frac{pA}{g}$$

Answer 2

Performing the same calculations with the same values I obtain approximately 1275 kg. Hence there must be at least an arithmetic error in your calculations.

As Dave Tweed pointed out in his answer, this is not the correct calculation to obtain the tensile force required to cause failure. The correct calculation results in about 130 kg.

That isn't unreasonable if the adhesive is loaded purely in tension. However, if the load is slightly off center, or there is a torque, then the adhesive will be loaded unevenly and begin to fail at one end first. Once the adhesive has failed at a corner or edge, the remaining adhesive will have higher stress and failure will occur more rapidly. Adhesives tend to fail by peeling more readily than in pure tension. Peel strength is generally a more useful measure of adhesive strength, as adhesives tend to fail by peel long before they fail in tension.