# How to calculate strength for titanium wire

I'd like to use a titanium wire to make some jewelry. I ordered two kinds of titanium wire, 0.3mm thick and 0.5mm thick. Both of them are grade 1 titanium.

How do I calculate the strength they'll have, i.e. the amount of weight they could lift before snapping?

I know that titanium grade 1 has an ultimate tensile strength of 240 MPa, but I don't know how to use that information to get the amount of force needed to snap the wire.

Stress = Force / Area, and "tensile strength" really means "tensile stress".

You need to be careful with units (and some people would recommend always convert everything into "basic SI units" of meters and Pascals), but using MPa and mm conveniently gives the force in Newtons.

The cross section area of your thin wire is $$3.14 \times 0.3 \times 0.3 \,/\, 4 = 0.07065$$ square mm, so the force to snap the wire is $$0.07065 \times 240 = 16.956$$ Newtons, or a weight of $$16.956 / 9.81 = 1.73$$ Kg.

For the thicker wire the force is $$4.8$$ Kg.

Note these are only approximate. You want to have a safety factor of at least 2, and maybe as high as 5, so the safe weights might be more like 350 grams and 960 grams.

The best thing to do would be attach something weighing that amount to a bit of wire, handle it roughly (for example jerk the wire rather than picking it up carefully) and convince yourself it isn't going to break before you start creating your jewellery.

• In my opinion is not safe to work with UTS, because the material will permanently deform at that stress up to at least 25% of its original length. – Sam Farjamirad Oct 20 '18 at 18:55
• Titanium is pretty close to elastic-perfectly plastic, so the elastic stress limit and the UTS are almost the same. This data sheet asm.matweb.com/search/SpecificMaterial.asp?bassnum=mtu010 gives the UTS as 240 MPa but the yield stress in the range of 170 to 310 (i.e it may break before it goes plastic - and I've seen that happen in aerospace grade titanium alloys) A safety factor of 5 on the UTS should be plenty, unless the jewellery is a safety-critical device! Compare with a ductile material like mild steel, where the UTS is about 850 MPa but the yield stress is only 250. – alephzero Oct 20 '18 at 19:09
• … I once learned the hard way how "non-plastic" titanium alloys can be, after redesigning a containment system to use titanium instead of mild steel to save weight. The containment part worked fine, but after the impact the titanium casing continued to "ring like a bell" literally for several minutes before the energy dissipated. WIth mild steel, you got a big plastically deformed bulge in the casing, and after a few seconds there was nothing happening any more. – alephzero Oct 20 '18 at 19:27
• Grade 1 should elongate /stretch more than 20% before fracture, being the most ductile and lowest strength grade. As noted the yield strength will be significantly lower than the UTS. – blacksmith37 Oct 21 '18 at 1:50
• @blacksmith37 "as noted" where? The material properties I referenced for Grade 1 give the UTS in the middle of the range of yield strengths, not "significantly lower". – alephzero Oct 21 '18 at 8:47