# Aluminum tube expansion (flaring)

Can anyone point me to a calculation or formula that would tell me what percentage an 6061 T6 aluminum tube OD should be able to be flared to, using any or all of the following: OD size, Wall size, yield strength, ultimate tensile strength and elongation?

I have a 3" long sample that has a 2" outside diameter with a wall size of 0.090". The method of flaring is utilizing an Instron tensile testing machine. The part is being forced down onto a 60 degree cone with a flat surface at the top. There is not a predetermined speed or force that the cross-head must move. The T, Y & E properties fall into the middle of the tolerance for the alloy and temper.

I realize the calculation couldn't be precise, but I'm wanting a ballpark figure to work with as my customers include a minimum flaring percentage that the part must make and I don't know where they're getting their data from. They are coming from steel so I want to make sure they are not just bringing that measurement straight across.

The typical part is anywhere from 2" to 3.5" OD with a wall in a range from .075" to 0.100".. The customer's spec for minimum flare percentage is from 10% to 15% depending on the part.

• It depends on more than just that... What temperature/environment are you doing this in? Expanded how gradually, i.e. how extreme is the taper? – Jonathan R Swift Sep 20 '18 at 18:16
• Just to check if we are in the same page, you mean if you pressurise the tube then what would be the ratio of the end OD to the original OD ? – Sam Farjamirad Sep 20 '18 at 18:16
• There are brake pipe flaring tools designed for copper, but only for the end to make a joint - are you talking about the whole length or just the end? – Solar Mike Sep 20 '18 at 19:02
• Hi: you may find much more useful answers if you describe what the end result is you are looking for , rather than how to get there. For example, there might be better ways to produce the "expanded" tubing, or it might be that material other than aluminum is far preferable to meet your system needs. – Carl Witthoft Sep 20 '18 at 19:39
• Add this information to your original question, because it is labelled as to broad and it's at the verge of closing, but it is a good question. – Sam Farjamirad Sep 21 '18 at 7:43

Though there are numerous rules of thumb used by manufacturers, a rigorous approach to finding an optimal amount of flare for a given geometry requires numerical solutions.

The simplest of these solutions will typical use von Mises plasticity (J2-plasticity) in conjunction with a damage model such as Johnson-Cook model.

An axisymmetric model (2D) will give you the plastic strains in the part but will not be able to predict tensile failures around the circumference. A random distribution of initial material parameters is needed to generate strain localization prior to failure.

Often it is easier for the manufacturer to just test a few samples rather than do numerical simulations for which there may not be in-house expertise.

Below, I've attached a few images of what a simulation might produce. Consider the axisymmetric case first. The initial condition is shown below.

If there is a lot of friction between the punch and the cylinder, you may get a buckled part (see below)

If friction is low, you will see flaring. Typically, a plastic strain of 0.25 - 0.5 is enough to cause tensile failure in 6061-T6 Al.

A better estimate can be found by doing a 3D simulation. See the figure below for a feel of what you will see.

There are many studies in the literature on the subject. A few recent ones are:

1) "A theoretical study of the expansion metal tubes" by Liu and Qiu, International Journal of Mechanical Sciences 114 (2016) 157–165.

2) "Towards the characterization of fracture in thin-walled tube forming" by Centeno et al., International Journal of Mechanical Sciences 119 (2016) 12–22.

3) "Numerical and experimental study of axial splitting of circular tubular structures" by Rouzegar and Karimi, Thin-Walled Structures 105 (2016) 57–70.

4) "Expansion and reduction of thin-walled tubes using a die:Experimental and theoretical investigation" by Almeida et al., International Journal of Machine Tools & Manufacture 46 (2006) 1643–1652.

You will get a good idea about the state of the art in this field in these papers.

• Thanks Biswajit, I will definitely look up the references you've posted. In my business, we haven't had the extrusion die built before receiving the quote, as dies are \$1,000s of dollars, for a part we may not get. So, a challenge we face is that we can't do testing in house prior to needing to decide whether or not to take the business on. This particular customer was one of the first in the US to switch from steel to aluminum. Its been a struggle convincing folks of the limits of this alloy and temper. – Jimmy V Sep 24 '18 at 12:55
• Added to the previous, the customer and the customer's customer will consider the entire lot of material non-conforming if only one sample is found to have a split. We may send thousands of feet of tube, but just one 2" sample split can cause major headaches and returns as they don't deal with a ppm, but a zero-defect policy. – Jimmy V Sep 24 '18 at 13:13
• In that case I'd recommend doing simulations. 6061-T6 is well characterized and you'll be able to find data quite easily. Tensile splits are caused by tiny imperfections in the shape and small variations in material properties. These cannot be avoided if you're working close to the limiting strength of the material. The solution is to work well below that strength, use a slow process (for low strain rates), and make sure that the tube extrusion process does not introduce too much texture in the tubes. – Biswajit Banerjee Sep 24 '18 at 20:53